[ { "task": "bearing_computation", "point_a": { "lat": 31.72888, "lon": 34.74632, "name": "Qiryat Mal’akhi" }, "point_b": { "lat": 53.73953, "lon": 78.04387, "name": "Karasuk" }, "ground_truth": { "initial_bearing_deg": 41.44, "cardinal_direction": "NE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Qiryat Mal’akhi at (31.72888°, 34.74632°)", " To: Karasuk at (53.73953°, 78.04387°)", "Step 2: Calculate longitude difference", " Δlon = 78.04387 - 34.74632 = 43.2976°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 41.44°", "Step 5: Determine cardinal direction", " 41.4° → NE", "FINAL ANSWER: 41.44° (NE)" ] }, { "task": "bearing_computation", "point_a": { "lat": 16.70836, "lon": 95.9336, "name": "Twante" }, "point_b": { "lat": -22.36611, "lon": -48.38028, "name": "Dois Córregos" }, "ground_truth": { "initial_bearing_deg": 254.61, "cardinal_direction": "W", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Twante at (16.70836°, 95.9336°)", " To: Dois Córregos at (-22.36611°, -48.38028°)", "Step 2: Calculate longitude difference", " Δlon = -48.38028 - 95.9336 = -144.3139°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 254.61°", "Step 5: Determine cardinal direction", " 254.6° → W", "FINAL ANSWER: 254.61° (W)" ] }, { "task": "bearing_computation", "point_a": { "lat": 29.86632, "lon": 77.89118, "name": "Roorkee" }, "point_b": { "lat": -37.84205, "lon": 145.0694, "name": "Camberwell" }, "ground_truth": { "initial_bearing_deg": 133.24, "cardinal_direction": "SE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Roorkee at (29.86632°, 77.89118°)", " To: Camberwell at (-37.84205°, 145.0694°)", "Step 2: Calculate longitude difference", " Δlon = 145.0694 - 77.89118 = 67.1782°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 133.24°", "Step 5: Determine cardinal direction", " 133.2° → SE", "FINAL ANSWER: 133.24° (SE)" ] }, { "task": "bearing_computation", "point_a": { "lat": 30.20942, "lon": -9.37922, "name": "Tine Biougra" }, "point_b": { "lat": 45.63873, "lon": -122.66149, "name": "Vancouver" }, "ground_truth": { "initial_bearing_deg": 319.68, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Tine Biougra at (30.20942°, -9.37922°)", " To: Vancouver at (45.63873°, -122.66149°)", "Step 2: Calculate longitude difference", " Δlon = -122.66149 - -9.37922 = -113.2823°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 319.68°", "Step 5: Determine cardinal direction", " 319.7° → NW", "FINAL ANSWER: 319.68° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": -18.14307, "lon": 177.50691, "name": "Sigatoka" }, "point_b": { "lat": 12.24922, "lon": -0.61527, "name": "Zorgo" }, "ground_truth": { "initial_bearing_deg": 197.35, "cardinal_direction": "S", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Sigatoka at (-18.14307°, 177.50691°)", " To: Zorgo at (12.24922°, -0.61527°)", "Step 2: Calculate longitude difference", " Δlon = -0.61527 - 177.50691 = -178.1222°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 197.35°", "Step 5: Determine cardinal direction", " 197.3° → S", "FINAL ANSWER: 197.35° (S)" ] }, { "task": "bearing_computation", "point_a": { "lat": 26.13421, "lon": -80.23184, "name": "Plantation" }, "point_b": { "lat": 40.68496, "lon": -80.10714, "name": "Cranberry Township" }, "ground_truth": { "initial_bearing_deg": 0.38, "cardinal_direction": "N", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Plantation at (26.13421°, -80.23184°)", " To: Cranberry Township at (40.68496°, -80.10714°)", "Step 2: Calculate longitude difference", " Δlon = -80.10714 - -80.23184 = 0.1247°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 0.38°", "Step 5: Determine cardinal direction", " 0.4° → N", "FINAL ANSWER: 0.38° (N)" ] }, { "task": "bearing_computation", "point_a": { "lat": -23.55108, "lon": -46.53829, "name": "Carrao" }, "point_b": { "lat": -5.04098, "lon": 18.81619, "name": "Kikwit" }, "ground_truth": { "initial_bearing_deg": 84.61, "cardinal_direction": "E", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Carrao at (-23.55108°, -46.53829°)", " To: Kikwit at (-5.04098°, 18.81619°)", "Step 2: Calculate longitude difference", " Δlon = 18.81619 - -46.53829 = 65.3545°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 84.61°", "Step 5: Determine cardinal direction", " 84.6° → E", "FINAL ANSWER: 84.61° (E)" ] }, { "task": "bearing_computation", "point_a": { "lat": 13.95, "lon": 40.66667, "name": "Arerti" }, "point_b": { "lat": 24.47979, "lon": 118.08187, "name": "Xiamen" }, "ground_truth": { "initial_bearing_deg": 68.25, "cardinal_direction": "E", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Arerti at (13.95°, 40.66667°)", " To: Xiamen at (24.47979°, 118.08187°)", "Step 2: Calculate longitude difference", " Δlon = 118.08187 - 40.66667 = 77.4152°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 68.25°", "Step 5: Determine cardinal direction", " 68.2° → E", "FINAL ANSWER: 68.25° (E)" ] }, { "task": "bearing_computation", "point_a": { "lat": 43.98333, "lon": 25.33333, "name": "Alexandria" }, "point_b": { "lat": 54.66079, "lon": -5.66802, "name": "Bangor" }, "ground_truth": { "initial_bearing_deg": 309.16, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Alexandria at (43.98333°, 25.33333°)", " To: Bangor at (54.66079°, -5.66802°)", "Step 2: Calculate longitude difference", " Δlon = -5.66802 - 25.33333 = -31.0014°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 309.16°", "Step 5: Determine cardinal direction", " 309.2° → NW", "FINAL ANSWER: 309.16° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": -28.72472, "lon": -52.84972, "name": "Espumoso" }, "point_b": { "lat": 50.90395, "lon": -1.40428, "name": "Southampton" }, "ground_truth": { "initial_bearing_deg": 29.56, "cardinal_direction": "NE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Espumoso at (-28.72472°, -52.84972°)", " To: Southampton at (50.90395°, -1.40428°)", "Step 2: Calculate longitude difference", " Δlon = -1.40428 - -52.84972 = 51.4454°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 29.56°", "Step 5: Determine cardinal direction", " 29.6° → NE", "FINAL ANSWER: 29.56° (NE)" ] }, { "task": "bearing_computation", "point_a": { "lat": 10.38542, "lon": -9.30568, "name": "Kankan" }, "point_b": { "lat": 24.74745, "lon": 67.92353, "name": "Thatta" }, "ground_truth": { "initial_bearing_deg": 67.02, "cardinal_direction": "NE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Kankan at (10.38542°, -9.30568°)", " To: Thatta at (24.74745°, 67.92353°)", "Step 2: Calculate longitude difference", " Δlon = 67.92353 - -9.30568 = 77.2292°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 67.02°", "Step 5: Determine cardinal direction", " 67.0° → NE", "FINAL ANSWER: 67.02° (NE)" ] }, { "task": "bearing_computation", "point_a": { "lat": -33.28397, "lon": 149.10018, "name": "Orange" }, "point_b": { "lat": -37.87709, "lon": 145.12939, "name": "Mount Waverley" }, "ground_truth": { "initial_bearing_deg": 213.97, "cardinal_direction": "SW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Orange at (-33.28397°, 149.10018°)", " To: Mount Waverley at (-37.87709°, 145.12939°)", "Step 2: Calculate longitude difference", " Δlon = 145.12939 - 149.10018 = -3.9708°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 213.97°", "Step 5: Determine cardinal direction", " 214.0° → SW", "FINAL ANSWER: 213.97° (SW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 28.92313, "lon": -13.66579, "name": "Puerto del Carmen" }, "point_b": { "lat": 46.61667, "lon": 14.28333, "name": "Sankt Martin" }, "ground_truth": { "initial_bearing_deg": 43.21, "cardinal_direction": "NE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Puerto del Carmen at (28.92313°, -13.66579°)", " To: Sankt Martin at (46.61667°, 14.28333°)", "Step 2: Calculate longitude difference", " Δlon = 14.28333 - -13.66579 = 27.9491°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 43.21°", "Step 5: Determine cardinal direction", " 43.2° → NE", "FINAL ANSWER: 43.21° (NE)" ] }, { "task": "bearing_computation", "point_a": { "lat": 37.57444, "lon": 43.74083, "name": "Hakkâri" }, "point_b": { "lat": 32.12722, "lon": 112.75417, "name": "Zaoyang" }, "ground_truth": { "initial_bearing_deg": 73.35, "cardinal_direction": "E", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Hakkâri at (37.57444°, 43.74083°)", " To: Zaoyang at (32.12722°, 112.75417°)", "Step 2: Calculate longitude difference", " Δlon = 112.75417 - 43.74083 = 69.0133°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 73.35°", "Step 5: Determine cardinal direction", " 73.3° → E", "FINAL ANSWER: 73.35° (E)" ] }, { "task": "bearing_computation", "point_a": { "lat": 9.86142, "lon": -84.09266, "name": "Aserrí" }, "point_b": { "lat": -4.04167, "lon": -44.475, "name": "São Mateus do Maranhão" }, "ground_truth": { "initial_bearing_deg": 107.54, "cardinal_direction": "E", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Aserrí at (9.86142°, -84.09266°)", " To: São Mateus do Maranhão at (-4.04167°, -44.475°)", "Step 2: Calculate longitude difference", " Δlon = -44.475 - -84.09266 = 39.6177°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 107.54°", "Step 5: Determine cardinal direction", " 107.5° → E", "FINAL ANSWER: 107.54° (E)" ] }, { "task": "bearing_computation", "point_a": { "lat": 30.0362, "lon": 47.91951, "name": "Umm Qaşr" }, "point_b": { "lat": 38.99817, "lon": -77.28832, "name": "Great Falls" }, "ground_truth": { "initial_bearing_deg": 320.45, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Umm Qaşr at (30.0362°, 47.91951°)", " To: Great Falls at (38.99817°, -77.28832°)", "Step 2: Calculate longitude difference", " Δlon = -77.28832 - 47.91951 = -125.2078°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 320.45°", "Step 5: Determine cardinal direction", " 320.4° → NW", "FINAL ANSWER: 320.45° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 43.18944, "lon": 141.00222, "name": "Otaru" }, "point_b": { "lat": -25.76972, "lon": -49.71583, "name": "Lapa" }, "ground_truth": { "initial_bearing_deg": 30.13, "cardinal_direction": "NE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Otaru at (43.18944°, 141.00222°)", " To: Lapa at (-25.76972°, -49.71583°)", "Step 2: Calculate longitude difference", " Δlon = -49.71583 - 141.00222 = -190.7181°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 30.13°", "Step 5: Determine cardinal direction", " 30.1° → NE", "FINAL ANSWER: 30.13° (NE)" ] }, { "task": "bearing_computation", "point_a": { "lat": 35.93333, "lon": 140.55, "name": "Itako" }, "point_b": { "lat": -1.04576, "lon": -80.65889, "name": "Montecristi" }, "ground_truth": { "initial_bearing_deg": 57.07, "cardinal_direction": "NE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Itako at (35.93333°, 140.55°)", " To: Montecristi at (-1.04576°, -80.65889°)", "Step 2: Calculate longitude difference", " Δlon = -80.65889 - 140.55 = -221.2089°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 57.07°", "Step 5: Determine cardinal direction", " 57.1° → NE", "FINAL ANSWER: 57.07° (NE)" ] }, { "task": "bearing_computation", "point_a": { "lat": -33.85, "lon": 151.03333, "name": "Auburn" }, "point_b": { "lat": -28.29917, "lon": -54.26306, "name": "Santo Ângelo" }, "ground_truth": { "initial_bearing_deg": 155.8, "cardinal_direction": "SE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Auburn at (-33.85°, 151.03333°)", " To: Santo Ângelo at (-28.29917°, -54.26306°)", "Step 2: Calculate longitude difference", " Δlon = -54.26306 - 151.03333 = -205.2964°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 155.80°", "Step 5: Determine cardinal direction", " 155.8° → SE", "FINAL ANSWER: 155.80° (SE)" ] }, { "task": "bearing_computation", "point_a": { "lat": 43.93064, "lon": 10.92365, "name": "Pistoia" }, "point_b": { "lat": 39.34474, "lon": 16.23802, "name": "Quattromiglia" }, "ground_truth": { "initial_bearing_deg": 137.31, "cardinal_direction": "SE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Pistoia at (43.93064°, 10.92365°)", " To: Quattromiglia at (39.34474°, 16.23802°)", "Step 2: Calculate longitude difference", " Δlon = 16.23802 - 10.92365 = 5.3144°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 137.31°", "Step 5: Determine cardinal direction", " 137.3° → SE", "FINAL ANSWER: 137.31° (SE)" ] }, { "task": "bearing_computation", "point_a": { "lat": 32.65236, "lon": -8.42769, "name": "Sidi Bennour" }, "point_b": { "lat": 11.70611, "lon": 122.36444, "name": "Kalibo (poblacion)" }, "ground_truth": { "initial_bearing_deg": 55.16, "cardinal_direction": "NE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Sidi Bennour at (32.65236°, -8.42769°)", " To: Kalibo (poblacion) at (11.70611°, 122.36444°)", "Step 2: Calculate longitude difference", " Δlon = 122.36444 - -8.42769 = 130.7921°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 55.16°", "Step 5: Determine cardinal direction", " 55.2° → NE", "FINAL ANSWER: 55.16° (NE)" ] }, { "task": "bearing_computation", "point_a": { "lat": 11.52134, "lon": 13.68952, "name": "Bama" }, "point_b": { "lat": 36.72016, "lon": -4.42034, "name": "Málaga" }, "ground_truth": { "initial_bearing_deg": 330.12, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Bama at (11.52134°, 13.68952°)", " To: Málaga at (36.72016°, -4.42034°)", "Step 2: Calculate longitude difference", " Δlon = -4.42034 - 13.68952 = -18.1099°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 330.12°", "Step 5: Determine cardinal direction", " 330.1° → NW", "FINAL ANSWER: 330.12° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": -22.54861, "lon": -47.91389, "name": "São Pedro" }, "point_b": { "lat": -34.49459, "lon": -58.62729, "name": "Don Torcuato" }, "ground_truth": { "initial_bearing_deg": 215.79, "cardinal_direction": "SW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: São Pedro at (-22.54861°, -47.91389°)", " To: Don Torcuato at (-34.49459°, -58.62729°)", "Step 2: Calculate longitude difference", " Δlon = -58.62729 - -47.91389 = -10.7134°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 215.79°", "Step 5: Determine cardinal direction", " 215.8° → SW", "FINAL ANSWER: 215.79° (SW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 35.70915, "lon": 10.67397, "name": "Ouardenine" }, "point_b": { "lat": 48.7606, "lon": 8.23975, "name": "Baden-Baden" }, "ground_truth": { "initial_bearing_deg": 352.94, "cardinal_direction": "N", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Ouardenine at (35.70915°, 10.67397°)", " To: Baden-Baden at (48.7606°, 8.23975°)", "Step 2: Calculate longitude difference", " Δlon = 8.23975 - 10.67397 = -2.4342°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 352.94°", "Step 5: Determine cardinal direction", " 352.9° → N", "FINAL ANSWER: 352.94° (N)" ] }, { "task": "bearing_computation", "point_a": { "lat": 52.20667, "lon": 104.2177, "name": "Markova" }, "point_b": { "lat": 24.55524, "lon": -81.78163, "name": "Key West" }, "ground_truth": { "initial_bearing_deg": 5.6, "cardinal_direction": "N", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Markova at (52.20667°, 104.2177°)", " To: Key West at (24.55524°, -81.78163°)", "Step 2: Calculate longitude difference", " Δlon = -81.78163 - 104.2177 = -185.9993°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 5.60°", "Step 5: Determine cardinal direction", " 5.6° → N", "FINAL ANSWER: 5.60° (N)" ] }, { "task": "bearing_computation", "point_a": { "lat": 37.16911, "lon": 10.03478, "name": "El Alia" }, "point_b": { "lat": 7.90303, "lon": 4.31364, "name": "Ejigbo" }, "ground_truth": { "initial_bearing_deg": 191.49, "cardinal_direction": "S", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: El Alia at (37.16911°, 10.03478°)", " To: Ejigbo at (7.90303°, 4.31364°)", "Step 2: Calculate longitude difference", " Δlon = 4.31364 - 10.03478 = -5.7211°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 191.49°", "Step 5: Determine cardinal direction", " 191.5° → S", "FINAL ANSWER: 191.49° (S)" ] }, { "task": "bearing_computation", "point_a": { "lat": 17.67178, "lon": 74.01289, "name": "Godoli" }, "point_b": { "lat": 56.56699, "lon": 9.02707, "name": "Skive" }, "ground_truth": { "initial_bearing_deg": 325.43, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Godoli at (17.67178°, 74.01289°)", " To: Skive at (56.56699°, 9.02707°)", "Step 2: Calculate longitude difference", " Δlon = 9.02707 - 74.01289 = -64.9858°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 325.43°", "Step 5: Determine cardinal direction", " 325.4° → NW", "FINAL ANSWER: 325.43° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 19.6031, "lon": 74.19356, "name": "Ghulewadi" }, "point_b": { "lat": -37.71893, "lon": -72.24099, "name": "Mulchén" }, "ground_truth": { "initial_bearing_deg": 230.92, "cardinal_direction": "SW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Ghulewadi at (19.6031°, 74.19356°)", " To: Mulchén at (-37.71893°, -72.24099°)", "Step 2: Calculate longitude difference", " Δlon = -72.24099 - 74.19356 = -146.4346°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 230.92°", "Step 5: Determine cardinal direction", " 230.9° → SW", "FINAL ANSWER: 230.92° (SW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 14.10594, "lon": -15.5508, "name": "Kaffrine" }, "point_b": { "lat": 31.18352, "lon": 30.52448, "name": "Al Maḩmūdīyah" }, "ground_truth": { "initial_bearing_deg": 59.88, "cardinal_direction": "NE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Kaffrine at (14.10594°, -15.5508°)", " To: Al Maḩmūdīyah at (31.18352°, 30.52448°)", "Step 2: Calculate longitude difference", " Δlon = 30.52448 - -15.5508 = 46.0753°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 59.88°", "Step 5: Determine cardinal direction", " 59.9° → NE", "FINAL ANSWER: 59.88° (NE)" ] }, { "task": "bearing_computation", "point_a": { "lat": 57.7584, "lon": 16.63733, "name": "Västervik" }, "point_b": { "lat": -31.44957, "lon": -60.93153, "name": "Esperanza" }, "ground_truth": { "initial_bearing_deg": 242.5, "cardinal_direction": "SW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Västervik at (57.7584°, 16.63733°)", " To: Esperanza at (-31.44957°, -60.93153°)", "Step 2: Calculate longitude difference", " Δlon = -60.93153 - 16.63733 = -77.5689°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 242.50°", "Step 5: Determine cardinal direction", " 242.5° → SW", "FINAL ANSWER: 242.50° (SW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 36.84666, "lon": 136.98355, "name": "Himi" }, "point_b": { "lat": 30.36846, "lon": 75.86791, "name": "Dhūri" }, "ground_truth": { "initial_bearing_deg": 281.57, "cardinal_direction": "W", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Himi at (36.84666°, 136.98355°)", " To: Dhūri at (30.36846°, 75.86791°)", "Step 2: Calculate longitude difference", " Δlon = 75.86791 - 136.98355 = -61.1156°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 281.57°", "Step 5: Determine cardinal direction", " 281.6° → W", "FINAL ANSWER: 281.57° (W)" ] }, { "task": "bearing_computation", "point_a": { "lat": 60.45148, "lon": 22.26869, "name": "Turku" }, "point_b": { "lat": 33.41477, "lon": -111.90931, "name": "Tempe" }, "ground_truth": { "initial_bearing_deg": 322.41, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Turku at (60.45148°, 22.26869°)", " To: Tempe at (33.41477°, -111.90931°)", "Step 2: Calculate longitude difference", " Δlon = -111.90931 - 22.26869 = -134.1780°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 322.41°", "Step 5: Determine cardinal direction", " 322.4° → NW", "FINAL ANSWER: 322.41° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": -20.83778, "lon": -40.72194, "name": "Piúma" }, "point_b": { "lat": 48.78421, "lon": 1.9552, "name": "Élancourt" }, "ground_truth": { "initial_bearing_deg": 27.03, "cardinal_direction": "NE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Piúma at (-20.83778°, -40.72194°)", " To: Élancourt at (48.78421°, 1.9552°)", "Step 2: Calculate longitude difference", " Δlon = 1.9552 - -40.72194 = 42.6771°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 27.03°", "Step 5: Determine cardinal direction", " 27.0° → NE", "FINAL ANSWER: 27.03° (NE)" ] }, { "task": "bearing_computation", "point_a": { "lat": -4.36667, "lon": 35.08333, "name": "Basotu" }, "point_b": { "lat": -0.40306, "lon": 31.15722, "name": "Lyantonde" }, "ground_truth": { "initial_bearing_deg": 315.2, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Basotu at (-4.36667°, 35.08333°)", " To: Lyantonde at (-0.40306°, 31.15722°)", "Step 2: Calculate longitude difference", " Δlon = 31.15722 - 35.08333 = -3.9261°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 315.20°", "Step 5: Determine cardinal direction", " 315.2° → NW", "FINAL ANSWER: 315.20° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": -22.98436, "lon": -43.20285, "name": "Ipanema" }, "point_b": { "lat": 45.81516, "lon": 19.6318, "name": "Bačka Topola" }, "ground_truth": { "initial_bearing_deg": 38.33, "cardinal_direction": "NE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Ipanema at (-22.98436°, -43.20285°)", " To: Bačka Topola at (45.81516°, 19.6318°)", "Step 2: Calculate longitude difference", " Δlon = 19.6318 - -43.20285 = 62.8346°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 38.33°", "Step 5: Determine cardinal direction", " 38.3° → NE", "FINAL ANSWER: 38.33° (NE)" ] }, { "task": "bearing_computation", "point_a": { "lat": 38.24719, "lon": 125.79476, "name": "Ayang-ni" }, "point_b": { "lat": -19.9, "lon": 47.23333, "name": "Soanindrariny" }, "ground_truth": { "initial_bearing_deg": 247.45, "cardinal_direction": "SW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Ayang-ni at (38.24719°, 125.79476°)", " To: Soanindrariny at (-19.9°, 47.23333°)", "Step 2: Calculate longitude difference", " Δlon = 47.23333 - 125.79476 = -78.5614°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 247.45°", "Step 5: Determine cardinal direction", " 247.4° → SW", "FINAL ANSWER: 247.45° (SW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 27.06193, "lon": -101.54891, "name": "San Buenaventura" }, "point_b": { "lat": 38.50839, "lon": -90.32289, "name": "Mehlville" }, "ground_truth": { "initial_bearing_deg": 36.58, "cardinal_direction": "NE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: San Buenaventura at (27.06193°, -101.54891°)", " To: Mehlville at (38.50839°, -90.32289°)", "Step 2: Calculate longitude difference", " Δlon = -90.32289 - -101.54891 = 11.2260°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 36.58°", "Step 5: Determine cardinal direction", " 36.6° → NE", "FINAL ANSWER: 36.58° (NE)" ] }, { "task": "bearing_computation", "point_a": { "lat": 21.68216, "lon": -78.62567, "name": "Baraguá" }, "point_b": { "lat": 20.66667, "lon": -88.56667, "name": "Chichén-Itzá" }, "ground_truth": { "initial_bearing_deg": 265.56, "cardinal_direction": "W", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Baraguá at (21.68216°, -78.62567°)", " To: Chichén-Itzá at (20.66667°, -88.56667°)", "Step 2: Calculate longitude difference", " Δlon = -88.56667 - -78.62567 = -9.9410°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 265.56°", "Step 5: Determine cardinal direction", " 265.6° → W", "FINAL ANSWER: 265.56° (W)" ] }, { "task": "bearing_computation", "point_a": { "lat": -5.04098, "lon": 18.81619, "name": "Kikwit" }, "point_b": { "lat": -27.18871, "lon": 25.32931, "name": "Schweizer-Reneke" }, "ground_truth": { "initial_bearing_deg": 165.04, "cardinal_direction": "S", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Kikwit at (-5.04098°, 18.81619°)", " To: Schweizer-Reneke at (-27.18871°, 25.32931°)", "Step 2: Calculate longitude difference", " Δlon = 25.32931 - 18.81619 = 6.5131°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 165.04°", "Step 5: Determine cardinal direction", " 165.0° → S", "FINAL ANSWER: 165.04° (S)" ] }, { "task": "bearing_computation", "point_a": { "lat": 34.67139, "lon": 70.20944, "name": "Mehtar Lām" }, "point_b": { "lat": -7.31473, "lon": 16.0024, "name": "Sanza Pombo" }, "ground_truth": { "initial_bearing_deg": 241.62, "cardinal_direction": "SW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Mehtar Lām at (34.67139°, 70.20944°)", " To: Sanza Pombo at (-7.31473°, 16.0024°)", "Step 2: Calculate longitude difference", " Δlon = 16.0024 - 70.20944 = -54.2070°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 241.62°", "Step 5: Determine cardinal direction", " 241.6° → SW", "FINAL ANSWER: 241.62° (SW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 9.8, "lon": 38.73333, "name": "Fichē" }, "point_b": { "lat": 7.15571, "lon": 3.34509, "name": "Abeokuta" }, "ground_truth": { "initial_bearing_deg": 268.51, "cardinal_direction": "W", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Fichē at (9.8°, 38.73333°)", " To: Abeokuta at (7.15571°, 3.34509°)", "Step 2: Calculate longitude difference", " Δlon = 3.34509 - 38.73333 = -35.3882°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 268.51°", "Step 5: Determine cardinal direction", " 268.5° → W", "FINAL ANSWER: 268.51° (W)" ] }, { "task": "bearing_computation", "point_a": { "lat": 50.965, "lon": 5.50082, "name": "Genk" }, "point_b": { "lat": 10.35028, "lon": 39.93626, "name": "Āt’aye" }, "ground_truth": { "initial_bearing_deg": 132.91, "cardinal_direction": "SE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Genk at (50.965°, 5.50082°)", " To: Āt’aye at (10.35028°, 39.93626°)", "Step 2: Calculate longitude difference", " Δlon = 39.93626 - 5.50082 = 34.4354°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 132.91°", "Step 5: Determine cardinal direction", " 132.9° → SE", "FINAL ANSWER: 132.91° (SE)" ] }, { "task": "bearing_computation", "point_a": { "lat": -3.49167, "lon": -45.25111, "name": "Monção" }, "point_b": { "lat": 13.4556, "lon": 109.22348, "name": "Sông Cầu" }, "ground_truth": { "initial_bearing_deg": 66.89, "cardinal_direction": "NE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Monção at (-3.49167°, -45.25111°)", " To: Sông Cầu at (13.4556°, 109.22348°)", "Step 2: Calculate longitude difference", " Δlon = 109.22348 - -45.25111 = 154.4746°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 66.89°", "Step 5: Determine cardinal direction", " 66.9° → NE", "FINAL ANSWER: 66.89° (NE)" ] }, { "task": "bearing_computation", "point_a": { "lat": 41.17289, "lon": -8.59931, "name": "Paranhos" }, "point_b": { "lat": -27.3171, "lon": 153.03097, "name": "Bracken Ridge" }, "ground_truth": { "initial_bearing_deg": 53.17, "cardinal_direction": "NE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Paranhos at (41.17289°, -8.59931°)", " To: Bracken Ridge at (-27.3171°, 153.03097°)", "Step 2: Calculate longitude difference", " Δlon = 153.03097 - -8.59931 = 161.6303°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 53.17°", "Step 5: Determine cardinal direction", " 53.2° → NE", "FINAL ANSWER: 53.17° (NE)" ] }, { "task": "bearing_computation", "point_a": { "lat": -11.72917, "lon": -49.06861, "name": "Gurupi" }, "point_b": { "lat": 22.75923, "lon": 113.79452, "name": "Gongheyong" }, "ground_truth": { "initial_bearing_deg": 53.69, "cardinal_direction": "NE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Gurupi at (-11.72917°, -49.06861°)", " To: Gongheyong at (22.75923°, 113.79452°)", "Step 2: Calculate longitude difference", " Δlon = 113.79452 - -49.06861 = 162.8631°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 53.69°", "Step 5: Determine cardinal direction", " 53.7° → NE", "FINAL ANSWER: 53.69° (NE)" ] }, { "task": "bearing_computation", "point_a": { "lat": 34.11849, "lon": -6.7389, "name": "Bouknadel" }, "point_b": { "lat": 59.34, "lon": 17.94, "name": "Bromma" }, "ground_truth": { "initial_bearing_deg": 25.21, "cardinal_direction": "NE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Bouknadel at (34.11849°, -6.7389°)", " To: Bromma at (59.34°, 17.94°)", "Step 2: Calculate longitude difference", " Δlon = 17.94 - -6.7389 = 24.6789°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 25.21°", "Step 5: Determine cardinal direction", " 25.2° → NE", "FINAL ANSWER: 25.21° (NE)" ] }, { "task": "bearing_computation", "point_a": { "lat": 32.7236, "lon": -5.1025, "name": "Boumia" }, "point_b": { "lat": 39.07195, "lon": -0.26623, "name": "Tavernes de la Valldigna" }, "ground_truth": { "initial_bearing_deg": 30.29, "cardinal_direction": "NE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Boumia at (32.7236°, -5.1025°)", " To: Tavernes de la Valldigna at (39.07195°, -0.26623°)", "Step 2: Calculate longitude difference", " Δlon = -0.26623 - -5.1025 = 4.8363°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 30.29°", "Step 5: Determine cardinal direction", " 30.3° → NE", "FINAL ANSWER: 30.29° (NE)" ] }, { "task": "bearing_computation", "point_a": { "lat": 39.76282, "lon": -86.39972, "name": "Avon" }, "point_b": { "lat": 3.6746, "lon": 100.9867, "name": "Sungai Besar" }, "ground_truth": { "initial_bearing_deg": 349.35, "cardinal_direction": "N", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Avon at (39.76282°, -86.39972°)", " To: Sungai Besar at (3.6746°, 100.9867°)", "Step 2: Calculate longitude difference", " Δlon = 100.9867 - -86.39972 = 187.3864°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 349.35°", "Step 5: Determine cardinal direction", " 349.4° → N", "FINAL ANSWER: 349.35° (N)" ] }, { "task": "bearing_computation", "point_a": { "lat": -21.13361, "lon": -51.10167, "name": "Mirandópolis" }, "point_b": { "lat": 6.19041, "lon": -67.48391, "name": "Puerto Carreño" }, "ground_truth": { "initial_bearing_deg": 327.75, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Mirandópolis at (-21.13361°, -51.10167°)", " To: Puerto Carreño at (6.19041°, -67.48391°)", "Step 2: Calculate longitude difference", " Δlon = -67.48391 - -51.10167 = -16.3822°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 327.75°", "Step 5: Determine cardinal direction", " 327.8° → NW", "FINAL ANSWER: 327.75° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 20.71373, "lon": 77.02639, "name": "Umbri" }, "point_b": { "lat": -43.89834, "lon": 171.73011, "name": "Ashburton" }, "ground_truth": { "initial_bearing_deg": 131.15, "cardinal_direction": "SE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Umbri at (20.71373°, 77.02639°)", " To: Ashburton at (-43.89834°, 171.73011°)", "Step 2: Calculate longitude difference", " Δlon = 171.73011 - 77.02639 = 94.7037°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 131.15°", "Step 5: Determine cardinal direction", " 131.2° → SE", "FINAL ANSWER: 131.15° (SE)" ] }, { "task": "bearing_computation", "point_a": { "lat": -9.53694, "lon": -36.63361, "name": "Igaci" }, "point_b": { "lat": -20.87222, "lon": -51.4875, "name": "Castilho" }, "ground_truth": { "initial_bearing_deg": 229.9, "cardinal_direction": "SW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Igaci at (-9.53694°, -36.63361°)", " To: Castilho at (-20.87222°, -51.4875°)", "Step 2: Calculate longitude difference", " Δlon = -51.4875 - -36.63361 = -14.8539°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 229.90°", "Step 5: Determine cardinal direction", " 229.9° → SW", "FINAL ANSWER: 229.90° (SW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 40.84394, "lon": 14.0952, "name": "Pozzuoli" }, "point_b": { "lat": 9.56667, "lon": 37.1, "name": "Shambu" }, "ground_truth": { "initial_bearing_deg": 140.52, "cardinal_direction": "SE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Pozzuoli at (40.84394°, 14.0952°)", " To: Shambu at (9.56667°, 37.1°)", "Step 2: Calculate longitude difference", " Δlon = 37.1 - 14.0952 = 23.0048°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 140.52°", "Step 5: Determine cardinal direction", " 140.5° → SE", "FINAL ANSWER: 140.52° (SE)" ] }, { "task": "bearing_computation", "point_a": { "lat": 49.19884, "lon": 9.5072, "name": "Öhringen" }, "point_b": { "lat": 78.22334, "lon": 15.64689, "name": "Longyearbyen" }, "ground_truth": { "initial_bearing_deg": 2.57, "cardinal_direction": "N", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Öhringen at (49.19884°, 9.5072°)", " To: Longyearbyen at (78.22334°, 15.64689°)", "Step 2: Calculate longitude difference", " Δlon = 15.64689 - 9.5072 = 6.1397°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 2.57°", "Step 5: Determine cardinal direction", " 2.6° → N", "FINAL ANSWER: 2.57° (N)" ] }, { "task": "bearing_computation", "point_a": { "lat": -33.71028, "lon": 150.95095, "name": "Kellyville" }, "point_b": { "lat": 43.70313, "lon": 7.26608, "name": "Nice" }, "ground_truth": { "initial_bearing_deg": 300.43, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Kellyville at (-33.71028°, 150.95095°)", " To: Nice at (43.70313°, 7.26608°)", "Step 2: Calculate longitude difference", " Δlon = 7.26608 - 150.95095 = -143.6849°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 300.43°", "Step 5: Determine cardinal direction", " 300.4° → NW", "FINAL ANSWER: 300.43° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": -2.94722, "lon": -48.95306, "name": "Tailândia" }, "point_b": { "lat": 17.66709, "lon": 82.61245, "name": "Narsīpatnam" }, "ground_truth": { "initial_bearing_deg": 69.22, "cardinal_direction": "E", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Tailândia at (-2.94722°, -48.95306°)", " To: Narsīpatnam at (17.66709°, 82.61245°)", "Step 2: Calculate longitude difference", " Δlon = 82.61245 - -48.95306 = 131.5655°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 69.22°", "Step 5: Determine cardinal direction", " 69.2° → E", "FINAL ANSWER: 69.22° (E)" ] }, { "task": "bearing_computation", "point_a": { "lat": 49.26667, "lon": 6.78333, "name": "Wadgassen" }, "point_b": { "lat": 11.46009, "lon": 78.18635, "name": "Rasipuram" }, "ground_truth": { "initial_bearing_deg": 96.58, "cardinal_direction": "E", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Wadgassen at (49.26667°, 6.78333°)", " To: Rasipuram at (11.46009°, 78.18635°)", "Step 2: Calculate longitude difference", " Δlon = 78.18635 - 6.78333 = 71.4030°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 96.58°", "Step 5: Determine cardinal direction", " 96.6° → E", "FINAL ANSWER: 96.58° (E)" ] }, { "task": "bearing_computation", "point_a": { "lat": 25.84341, "lon": 93.43116, "name": "Diphu" }, "point_b": { "lat": -35.41647, "lon": 149.06954, "name": "Tuggeranong Administrative District" }, "ground_truth": { "initial_bearing_deg": 137.03, "cardinal_direction": "SE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Diphu at (25.84341°, 93.43116°)", " To: Tuggeranong Administrative District at (-35.41647°, 149.06954°)", "Step 2: Calculate longitude difference", " Δlon = 149.06954 - 93.43116 = 55.6384°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 137.03°", "Step 5: Determine cardinal direction", " 137.0° → SE", "FINAL ANSWER: 137.03° (SE)" ] }, { "task": "bearing_computation", "point_a": { "lat": 4.08466, "lon": -76.19536, "name": "Tuluá" }, "point_b": { "lat": 27.31667, "lon": 103.71667, "name": "Zhaotong" }, "ground_truth": { "initial_bearing_deg": 0.15, "cardinal_direction": "N", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Tuluá at (4.08466°, -76.19536°)", " To: Zhaotong at (27.31667°, 103.71667°)", "Step 2: Calculate longitude difference", " Δlon = 103.71667 - -76.19536 = 179.9120°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 0.15°", "Step 5: Determine cardinal direction", " 0.1° → N", "FINAL ANSWER: 0.15° (N)" ] }, { "task": "bearing_computation", "point_a": { "lat": -34.424, "lon": 150.89345, "name": "Wollongong" }, "point_b": { "lat": 54.69981, "lon": 25.18393, "name": "Pilaitė" }, "ground_truth": { "initial_bearing_deg": 315.8, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Wollongong at (-34.424°, 150.89345°)", " To: Pilaitė at (54.69981°, 25.18393°)", "Step 2: Calculate longitude difference", " Δlon = 25.18393 - 150.89345 = -125.7095°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 315.80°", "Step 5: Determine cardinal direction", " 315.8° → NW", "FINAL ANSWER: 315.80° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": -37.0646, "lon": 174.94212, "name": "Papakura" }, "point_b": { "lat": 41.20917, "lon": 36.97389, "name": "Terme" }, "ground_truth": { "initial_bearing_deg": 290.56, "cardinal_direction": "W", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Papakura at (-37.0646°, 174.94212°)", " To: Terme at (41.20917°, 36.97389°)", "Step 2: Calculate longitude difference", " Δlon = 36.97389 - 174.94212 = -137.9682°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 290.56°", "Step 5: Determine cardinal direction", " 290.6° → W", "FINAL ANSWER: 290.56° (W)" ] }, { "task": "bearing_computation", "point_a": { "lat": 14.1951, "lon": 43.31518, "name": "Zabīd" }, "point_b": { "lat": -22.84278, "lon": -45.25139, "name": "Potim" }, "ground_truth": { "initial_bearing_deg": 247.48, "cardinal_direction": "SW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Zabīd at (14.1951°, 43.31518°)", " To: Potim at (-22.84278°, -45.25139°)", "Step 2: Calculate longitude difference", " Δlon = -45.25139 - 43.31518 = -88.5666°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 247.48°", "Step 5: Determine cardinal direction", " 247.5° → SW", "FINAL ANSWER: 247.48° (SW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 25.27143, "lon": 55.30207, "name": "Dayrah" }, "point_b": { "lat": 39.75895, "lon": -84.19161, "name": "Dayton" }, "ground_truth": { "initial_bearing_deg": 328.9, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Dayrah at (25.27143°, 55.30207°)", " To: Dayton at (39.75895°, -84.19161°)", "Step 2: Calculate longitude difference", " Δlon = -84.19161 - 55.30207 = -139.4937°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 328.90°", "Step 5: Determine cardinal direction", " 328.9° → NW", "FINAL ANSWER: 328.90° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 1.23889, "lon": 35.11194, "name": "Kapenguria" }, "point_b": { "lat": 41.74115, "lon": -87.61255, "name": "Chatham" }, "ground_truth": { "initial_bearing_deg": 317.05, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Kapenguria at (1.23889°, 35.11194°)", " To: Chatham at (41.74115°, -87.61255°)", "Step 2: Calculate longitude difference", " Δlon = -87.61255 - 35.11194 = -122.7245°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 317.05°", "Step 5: Determine cardinal direction", " 317.1° → NW", "FINAL ANSWER: 317.05° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": -3.20333, "lon": -52.20639, "name": "Altamira" }, "point_b": { "lat": 51.09242, "lon": 4.3717, "name": "Boom" }, "ground_truth": { "initial_bearing_deg": 33.36, "cardinal_direction": "NE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Altamira at (-3.20333°, -52.20639°)", " To: Boom at (51.09242°, 4.3717°)", "Step 2: Calculate longitude difference", " Δlon = 4.3717 - -52.20639 = 56.5781°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 33.36°", "Step 5: Determine cardinal direction", " 33.4° → NE", "FINAL ANSWER: 33.36° (NE)" ] }, { "task": "bearing_computation", "point_a": { "lat": -11.83268, "lon": 16.23613, "name": "Mungo" }, "point_b": { "lat": -11.26833, "lon": -37.43833, "name": "Estância" }, "ground_truth": { "initial_bearing_deg": 264.78, "cardinal_direction": "W", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Mungo at (-11.83268°, 16.23613°)", " To: Estância at (-11.26833°, -37.43833°)", "Step 2: Calculate longitude difference", " Δlon = -37.43833 - 16.23613 = -53.6745°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 264.78°", "Step 5: Determine cardinal direction", " 264.8° → W", "FINAL ANSWER: 264.78° (W)" ] }, { "task": "bearing_computation", "point_a": { "lat": 43.17124, "lon": -2.6338, "name": "Durango" }, "point_b": { "lat": 20.38983, "lon": 78.09027, "name": "Lohāra" }, "ground_truth": { "initial_bearing_deg": 80.75, "cardinal_direction": "E", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Durango at (43.17124°, -2.6338°)", " To: Lohāra at (20.38983°, 78.09027°)", "Step 2: Calculate longitude difference", " Δlon = 78.09027 - -2.6338 = 80.7241°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 80.75°", "Step 5: Determine cardinal direction", " 80.8° → E", "FINAL ANSWER: 80.75° (E)" ] }, { "task": "bearing_computation", "point_a": { "lat": 40.15669, "lon": 43.13424, "name": "Kağızman" }, "point_b": { "lat": 12.99809, "lon": 15.73195, "name": "Massakory" }, "ground_truth": { "initial_bearing_deg": 229.28, "cardinal_direction": "SW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Kağızman at (40.15669°, 43.13424°)", " To: Massakory at (12.99809°, 15.73195°)", "Step 2: Calculate longitude difference", " Δlon = 15.73195 - 43.13424 = -27.4023°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 229.28°", "Step 5: Determine cardinal direction", " 229.3° → SW", "FINAL ANSWER: 229.28° (SW)" ] }, { "task": "bearing_computation", "point_a": { "lat": -27.31472, "lon": -48.55917, "name": "Governador Celso Ramos" }, "point_b": { "lat": -38.82225, "lon": -68.06293, "name": "Cinco Saltos" }, "ground_truth": { "initial_bearing_deg": 229.77, "cardinal_direction": "SW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Governador Celso Ramos at (-27.31472°, -48.55917°)", " To: Cinco Saltos at (-38.82225°, -68.06293°)", "Step 2: Calculate longitude difference", " Δlon = -68.06293 - -48.55917 = -19.5038°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 229.77°", "Step 5: Determine cardinal direction", " 229.8° → SW", "FINAL ANSWER: 229.77° (SW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 13.737, "lon": 100.512, "name": "Samphanthawong" }, "point_b": { "lat": 19.26028, "lon": -99.59083, "name": "San Salvador Tizatlalli" }, "ground_truth": { "initial_bearing_deg": 31.43, "cardinal_direction": "NE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Samphanthawong at (13.737°, 100.512°)", " To: San Salvador Tizatlalli at (19.26028°, -99.59083°)", "Step 2: Calculate longitude difference", " Δlon = -99.59083 - 100.512 = -200.1028°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 31.43°", "Step 5: Determine cardinal direction", " 31.4° → NE", "FINAL ANSWER: 31.43° (NE)" ] }, { "task": "bearing_computation", "point_a": { "lat": 26.96667, "lon": 1.08333, "name": "Aoulef" }, "point_b": { "lat": 14.0775, "lon": -3.51594, "name": "Bankass" }, "ground_truth": { "initial_bearing_deg": 199.34, "cardinal_direction": "S", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Aoulef at (26.96667°, 1.08333°)", " To: Bankass at (14.0775°, -3.51594°)", "Step 2: Calculate longitude difference", " Δlon = -3.51594 - 1.08333 = -4.5993°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 199.34°", "Step 5: Determine cardinal direction", " 199.3° → S", "FINAL ANSWER: 199.34° (S)" ] }, { "task": "bearing_computation", "point_a": { "lat": 5.62611, "lon": 10.25421, "name": "Mbouda" }, "point_b": { "lat": 38.6703, "lon": 26.75656, "name": "Foça" }, "ground_truth": { "initial_bearing_deg": 22.02, "cardinal_direction": "N", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Mbouda at (5.62611°, 10.25421°)", " To: Foça at (38.6703°, 26.75656°)", "Step 2: Calculate longitude difference", " Δlon = 26.75656 - 10.25421 = 16.5023°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 22.02°", "Step 5: Determine cardinal direction", " 22.0° → N", "FINAL ANSWER: 22.02° (N)" ] }, { "task": "bearing_computation", "point_a": { "lat": -26.49155, "lon": 29.22878, "name": "Trichardt" }, "point_b": { "lat": 20.62268, "lon": -103.06813, "name": "Zapotlanejo" }, "ground_truth": { "initial_bearing_deg": 272.83, "cardinal_direction": "W", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Trichardt at (-26.49155°, 29.22878°)", " To: Zapotlanejo at (20.62268°, -103.06813°)", "Step 2: Calculate longitude difference", " Δlon = -103.06813 - 29.22878 = -132.2969°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 272.83°", "Step 5: Determine cardinal direction", " 272.8° → W", "FINAL ANSWER: 272.83° (W)" ] }, { "task": "bearing_computation", "point_a": { "lat": 41.2, "lon": -8.63333, "name": "São Tiago de Custoias" }, "point_b": { "lat": 45.46005, "lon": -73.57058, "name": "Verdun" }, "ground_truth": { "initial_bearing_deg": 298.19, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: São Tiago de Custoias at (41.2°, -8.63333°)", " To: Verdun at (45.46005°, -73.57058°)", "Step 2: Calculate longitude difference", " Δlon = -73.57058 - -8.63333 = -64.9373°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 298.19°", "Step 5: Determine cardinal direction", " 298.2° → NW", "FINAL ANSWER: 298.19° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": -21.15345, "lon": 149.16554, "name": "Mackay" }, "point_b": { "lat": -24.95911, "lon": 31.17025, "name": "Hlanganani" }, "ground_truth": { "initial_bearing_deg": 235.65, "cardinal_direction": "SW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Mackay at (-21.15345°, 149.16554°)", " To: Hlanganani at (-24.95911°, 31.17025°)", "Step 2: Calculate longitude difference", " Δlon = 31.17025 - 149.16554 = -117.9953°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 235.65°", "Step 5: Determine cardinal direction", " 235.7° → SW", "FINAL ANSWER: 235.65° (SW)" ] }, { "task": "bearing_computation", "point_a": { "lat": -27.03424, "lon": -65.30196, "name": "Bella Vista" }, "point_b": { "lat": 29.14816, "lon": 31.12733, "name": "Būsh" }, "ground_truth": { "initial_bearing_deg": 65.84, "cardinal_direction": "NE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Bella Vista at (-27.03424°, -65.30196°)", " To: Būsh at (29.14816°, 31.12733°)", "Step 2: Calculate longitude difference", " Δlon = 31.12733 - -65.30196 = 96.4293°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 65.84°", "Step 5: Determine cardinal direction", " 65.8° → NE", "FINAL ANSWER: 65.84° (NE)" ] }, { "task": "bearing_computation", "point_a": { "lat": 52.92343, "lon": 9.23491, "name": "Verden" }, "point_b": { "lat": -33.89743, "lon": 150.93446, "name": "Cabramatta" }, "ground_truth": { "initial_bearing_deg": 70.37, "cardinal_direction": "E", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Verden at (52.92343°, 9.23491°)", " To: Cabramatta at (-33.89743°, 150.93446°)", "Step 2: Calculate longitude difference", " Δlon = 150.93446 - 9.23491 = 141.6995°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 70.37°", "Step 5: Determine cardinal direction", " 70.4° → E", "FINAL ANSWER: 70.37° (E)" ] }, { "task": "bearing_computation", "point_a": { "lat": 20.27465, "lon": -76.95132, "name": "Yara" }, "point_b": { "lat": 47.79494, "lon": 124.45773, "name": "Fuyu" }, "ground_truth": { "initial_bearing_deg": 344.94, "cardinal_direction": "N", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Yara at (20.27465°, -76.95132°)", " To: Fuyu at (47.79494°, 124.45773°)", "Step 2: Calculate longitude difference", " Δlon = 124.45773 - -76.95132 = 201.4090°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 344.94°", "Step 5: Determine cardinal direction", " 344.9° → N", "FINAL ANSWER: 344.94° (N)" ] }, { "task": "bearing_computation", "point_a": { "lat": -17.29972, "lon": -48.27944, "name": "Pires do Rio" }, "point_b": { "lat": 1.3375, "lon": 103.90917, "name": "Kaki Bukit Estate" }, "ground_truth": { "initial_bearing_deg": 117.29, "cardinal_direction": "SE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Pires do Rio at (-17.29972°, -48.27944°)", " To: Kaki Bukit Estate at (1.3375°, 103.90917°)", "Step 2: Calculate longitude difference", " Δlon = 103.90917 - -48.27944 = 152.1886°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 117.29°", "Step 5: Determine cardinal direction", " 117.3° → SE", "FINAL ANSWER: 117.29° (SE)" ] }, { "task": "bearing_computation", "point_a": { "lat": -32.27682, "lon": 115.72978, "name": "Rockingham" }, "point_b": { "lat": 44.36548, "lon": 20.95885, "name": "Smederevska Palanka" }, "ground_truth": { "initial_bearing_deg": 308.14, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Rockingham at (-32.27682°, 115.72978°)", " To: Smederevska Palanka at (44.36548°, 20.95885°)", "Step 2: Calculate longitude difference", " Δlon = 20.95885 - 115.72978 = -94.7709°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 308.14°", "Step 5: Determine cardinal direction", " 308.1° → NW", "FINAL ANSWER: 308.14° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 42.34593, "lon": -71.55229, "name": "Marlborough" }, "point_b": { "lat": -3.50306, "lon": -80.27306, "name": "Zarumilla" }, "ground_truth": { "initial_bearing_deg": 192.04, "cardinal_direction": "S", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Marlborough at (42.34593°, -71.55229°)", " To: Zarumilla at (-3.50306°, -80.27306°)", "Step 2: Calculate longitude difference", " Δlon = -80.27306 - -71.55229 = -8.7208°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 192.04°", "Step 5: Determine cardinal direction", " 192.0° → S", "FINAL ANSWER: 192.04° (S)" ] }, { "task": "bearing_computation", "point_a": { "lat": -23.65094, "lon": -70.39752, "name": "Antofagasta" }, "point_b": { "lat": 12.95479, "lon": 36.15549, "name": "Metemma" }, "ground_truth": { "initial_bearing_deg": 84.26, "cardinal_direction": "E", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Antofagasta at (-23.65094°, -70.39752°)", " To: Metemma at (12.95479°, 36.15549°)", "Step 2: Calculate longitude difference", " Δlon = 36.15549 - -70.39752 = 106.5530°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 84.26°", "Step 5: Determine cardinal direction", " 84.3° → E", "FINAL ANSWER: 84.26° (E)" ] }, { "task": "bearing_computation", "point_a": { "lat": 36.50861, "lon": 32.08278, "name": "Kestel" }, "point_b": { "lat": 34.09205, "lon": 134.28452, "name": "Awa" }, "ground_truth": { "initial_bearing_deg": 55.58, "cardinal_direction": "NE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Kestel at (36.50861°, 32.08278°)", " To: Awa at (34.09205°, 134.28452°)", "Step 2: Calculate longitude difference", " Δlon = 134.28452 - 32.08278 = 102.2017°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 55.58°", "Step 5: Determine cardinal direction", " 55.6° → NE", "FINAL ANSWER: 55.58° (NE)" ] }, { "task": "bearing_computation", "point_a": { "lat": 2.2618, "lon": 102.2317, "name": "Kawasan Perindustrian Cheng" }, "point_b": { "lat": 31.31146, "lon": 31.14766, "name": "Al Ḩāmūl" }, "ground_truth": { "initial_bearing_deg": 302.17, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Kawasan Perindustrian Cheng at (2.2618°, 102.2317°)", " To: Al Ḩāmūl at (31.31146°, 31.14766°)", "Step 2: Calculate longitude difference", " Δlon = 31.14766 - 102.2317 = -71.0840°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 302.17°", "Step 5: Determine cardinal direction", " 302.2° → NW", "FINAL ANSWER: 302.17° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 40.42122, "lon": -3.61759, "name": "Arcos" }, "point_b": { "lat": 50.93331, "lon": 6.95954, "name": "Altstadt Sud" }, "ground_truth": { "initial_bearing_deg": 31.42, "cardinal_direction": "NE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Arcos at (40.42122°, -3.61759°)", " To: Altstadt Sud at (50.93331°, 6.95954°)", "Step 2: Calculate longitude difference", " Δlon = 6.95954 - -3.61759 = 10.5771°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 31.42°", "Step 5: Determine cardinal direction", " 31.4° → NE", "FINAL ANSWER: 31.42° (NE)" ] }, { "task": "bearing_computation", "point_a": { "lat": 27.61987, "lon": 80.20343, "name": "Pihānī" }, "point_b": { "lat": 40.41189, "lon": -3.65682, "name": "Media Legua" }, "ground_truth": { "initial_bearing_deg": 305.33, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Pihānī at (27.61987°, 80.20343°)", " To: Media Legua at (40.41189°, -3.65682°)", "Step 2: Calculate longitude difference", " Δlon = -3.65682 - 80.20343 = -83.8602°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 305.33°", "Step 5: Determine cardinal direction", " 305.3° → NW", "FINAL ANSWER: 305.33° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 48.53695, "lon": 9.2833, "name": "Metzingen" }, "point_b": { "lat": 10.47027, "lon": -66.61934, "name": "Guarenas" }, "ground_truth": { "initial_bearing_deg": 266.45, "cardinal_direction": "W", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Metzingen at (48.53695°, 9.2833°)", " To: Guarenas at (10.47027°, -66.61934°)", "Step 2: Calculate longitude difference", " Δlon = -66.61934 - 9.2833 = -75.9026°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 266.45°", "Step 5: Determine cardinal direction", " 266.4° → W", "FINAL ANSWER: 266.45° (W)" ] }, { "task": "bearing_computation", "point_a": { "lat": 43.80306, "lon": 143.89083, "name": "Kitami" }, "point_b": { "lat": -19.05294, "lon": -169.91957, "name": "Alofi" }, "ground_truth": { "initial_bearing_deg": 135.27, "cardinal_direction": "SE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Kitami at (43.80306°, 143.89083°)", " To: Alofi at (-19.05294°, -169.91957°)", "Step 2: Calculate longitude difference", " Δlon = -169.91957 - 143.89083 = -313.8104°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 135.27°", "Step 5: Determine cardinal direction", " 135.3° → SE", "FINAL ANSWER: 135.27° (SE)" ] }, { "task": "bearing_computation", "point_a": { "lat": -17.36667, "lon": 30.2, "name": "Chinhoyi" }, "point_b": { "lat": 48.92426, "lon": 2.2128, "name": "Bezons" }, "ground_truth": { "initial_bearing_deg": 340.94, "cardinal_direction": "N", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Chinhoyi at (-17.36667°, 30.2°)", " To: Bezons at (48.92426°, 2.2128°)", "Step 2: Calculate longitude difference", " Δlon = 2.2128 - 30.2 = -27.9872°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 340.94°", "Step 5: Determine cardinal direction", " 340.9° → N", "FINAL ANSWER: 340.94° (N)" ] }, { "task": "bearing_computation", "point_a": { "lat": 38.83861, "lon": 105.66861, "name": "Bayan Hot" }, "point_b": { "lat": 38.90524, "lon": -77.04362, "name": "Golden Triangle" }, "ground_truth": { "initial_bearing_deg": 2.16, "cardinal_direction": "N", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Bayan Hot at (38.83861°, 105.66861°)", " To: Golden Triangle at (38.90524°, -77.04362°)", "Step 2: Calculate longitude difference", " Δlon = -77.04362 - 105.66861 = -182.7122°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 2.16°", "Step 5: Determine cardinal direction", " 2.2° → N", "FINAL ANSWER: 2.16° (N)" ] }, { "task": "bearing_computation", "point_a": { "lat": -10.68333, "lon": 39.83333, "name": "Nanyamba" }, "point_b": { "lat": 1.94468, "lon": 30.03861, "name": "Mangbwalu" }, "ground_truth": { "initial_bearing_deg": 321.78, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Nanyamba at (-10.68333°, 39.83333°)", " To: Mangbwalu at (1.94468°, 30.03861°)", "Step 2: Calculate longitude difference", " Δlon = 30.03861 - 39.83333 = -9.7947°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 321.78°", "Step 5: Determine cardinal direction", " 321.8° → NW", "FINAL ANSWER: 321.78° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 51.90006, "lon": -2.07972, "name": "Cheltenham" }, "point_b": { "lat": 54.67501, "lon": 20.13473, "name": "Svetlyy" }, "ground_truth": { "initial_bearing_deg": 69.4, "cardinal_direction": "E", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Cheltenham at (51.90006°, -2.07972°)", " To: Svetlyy at (54.67501°, 20.13473°)", "Step 2: Calculate longitude difference", " Δlon = 20.13473 - -2.07972 = 22.2144°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 69.40°", "Step 5: Determine cardinal direction", " 69.4° → E", "FINAL ANSWER: 69.40° (E)" ] }, { "task": "bearing_computation", "point_a": { "lat": 44.103, "lon": 9.82375, "name": "La Spezia" }, "point_b": { "lat": 1.61549, "lon": -75.60412, "name": "Florencia" }, "ground_truth": { "initial_bearing_deg": 267.98, "cardinal_direction": "W", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: La Spezia at (44.103°, 9.82375°)", " To: Florencia at (1.61549°, -75.60412°)", "Step 2: Calculate longitude difference", " Δlon = -75.60412 - 9.82375 = -85.4279°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 267.98°", "Step 5: Determine cardinal direction", " 268.0° → W", "FINAL ANSWER: 267.98° (W)" ] }, { "task": "bearing_computation", "point_a": { "lat": 8.05861, "lon": -6.18972, "name": "Mankono" }, "point_b": { "lat": 41.97263, "lon": -71.32474, "name": "North Attleborough Center" }, "ground_truth": { "initial_bearing_deg": 312.51, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Mankono at (8.05861°, -6.18972°)", " To: North Attleborough Center at (41.97263°, -71.32474°)", "Step 2: Calculate longitude difference", " Δlon = -71.32474 - -6.18972 = -65.1350°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 312.51°", "Step 5: Determine cardinal direction", " 312.5° → NW", "FINAL ANSWER: 312.51° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 22.06566, "lon": 81.68543, "name": "Mungeli" }, "point_b": { "lat": 44.53889, "lon": 10.81166, "name": "Fiorano" }, "ground_truth": { "initial_bearing_deg": 309.86, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Mungeli at (22.06566°, 81.68543°)", " To: Fiorano at (44.53889°, 10.81166°)", "Step 2: Calculate longitude difference", " Δlon = 10.81166 - 81.68543 = -70.8738°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 309.86°", "Step 5: Determine cardinal direction", " 309.9° → NW", "FINAL ANSWER: 309.86° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 25.00827, "lon": 55.15682, "name": "Dubai Investments Park" }, "point_b": { "lat": 55.75, "lon": -4.03333, "name": "Meikle Earnock" }, "ground_truth": { "initial_bearing_deg": 322.38, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Dubai Investments Park at (25.00827°, 55.15682°)", " To: Meikle Earnock at (55.75°, -4.03333°)", "Step 2: Calculate longitude difference", " Δlon = -4.03333 - 55.15682 = -59.1902°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 322.38°", "Step 5: Determine cardinal direction", " 322.4° → NW", "FINAL ANSWER: 322.38° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 28.3769, "lon": 129.49379, "name": "Amami" }, "point_b": { "lat": 11.21266, "lon": 79.36369, "name": "Jayamkondacholapuram" }, "ground_truth": { "initial_bearing_deg": 260.37, "cardinal_direction": "W", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Amami at (28.3769°, 129.49379°)", " To: Jayamkondacholapuram at (11.21266°, 79.36369°)", "Step 2: Calculate longitude difference", " Δlon = 79.36369 - 129.49379 = -50.1301°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 260.37°", "Step 5: Determine cardinal direction", " 260.4° → W", "FINAL ANSWER: 260.37° (W)" ] }, { "task": "bearing_computation", "point_a": { "lat": 32.91851, "lon": -80.02203, "name": "Hanahan" }, "point_b": { "lat": -4.32861, "lon": -38.88472, "name": "Baturité" }, "ground_truth": { "initial_bearing_deg": 125.71, "cardinal_direction": "SE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Hanahan at (32.91851°, -80.02203°)", " To: Baturité at (-4.32861°, -38.88472°)", "Step 2: Calculate longitude difference", " Δlon = -38.88472 - -80.02203 = 41.1373°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 125.71°", "Step 5: Determine cardinal direction", " 125.7° → SE", "FINAL ANSWER: 125.71° (SE)" ] }, { "task": "bearing_computation", "point_a": { "lat": 29.2699, "lon": 51.2188, "name": "Borāzjān" }, "point_b": { "lat": 47.29722, "lon": -1.4921, "name": "Carquefou" }, "ground_truth": { "initial_bearing_deg": 309.21, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Borāzjān at (29.2699°, 51.2188°)", " To: Carquefou at (47.29722°, -1.4921°)", "Step 2: Calculate longitude difference", " Δlon = -1.4921 - 51.2188 = -52.7109°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 309.21°", "Step 5: Determine cardinal direction", " 309.2° → NW", "FINAL ANSWER: 309.21° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 22.24126, "lon": -80.3911, "name": "Palmira" }, "point_b": { "lat": 35.73289, "lon": 139.82085, "name": "Sumida" }, "ground_truth": { "initial_bearing_deg": 325.94, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Palmira at (22.24126°, -80.3911°)", " To: Sumida at (35.73289°, 139.82085°)", "Step 2: Calculate longitude difference", " Δlon = 139.82085 - -80.3911 = 220.2120°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 325.94°", "Step 5: Determine cardinal direction", " 325.9° → NW", "FINAL ANSWER: 325.94° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 46.87719, "lon": -96.7898, "name": "Fargo" }, "point_b": { "lat": -31.76737, "lon": 115.96936, "name": "Ellenbrook" }, "ground_truth": { "initial_bearing_deg": 289.4, "cardinal_direction": "W", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Fargo at (46.87719°, -96.7898°)", " To: Ellenbrook at (-31.76737°, 115.96936°)", "Step 2: Calculate longitude difference", " Δlon = 115.96936 - -96.7898 = 212.7592°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 289.40°", "Step 5: Determine cardinal direction", " 289.4° → W", "FINAL ANSWER: 289.40° (W)" ] }, { "task": "bearing_computation", "point_a": { "lat": 11.08155, "lon": 39.74339, "name": "Kombolcha" }, "point_b": { "lat": 41.66394, "lon": -83.55521, "name": "Toledo" }, "ground_truth": { "initial_bearing_deg": 319.5, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Kombolcha at (11.08155°, 39.74339°)", " To: Toledo at (41.66394°, -83.55521°)", "Step 2: Calculate longitude difference", " Δlon = -83.55521 - 39.74339 = -123.2986°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 319.50°", "Step 5: Determine cardinal direction", " 319.5° → NW", "FINAL ANSWER: 319.50° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 8.01714, "lon": 4.90421, "name": "Ila Orangun" }, "point_b": { "lat": 39.95373, "lon": -74.19792, "name": "Toms River" }, "ground_truth": { "initial_bearing_deg": 309.28, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Ila Orangun at (8.01714°, 4.90421°)", " To: Toms River at (39.95373°, -74.19792°)", "Step 2: Calculate longitude difference", " Δlon = -74.19792 - 4.90421 = -79.1021°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 309.28°", "Step 5: Determine cardinal direction", " 309.3° → NW", "FINAL ANSWER: 309.28° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 30.96187, "lon": 108.24327, "name": "Nanmen" }, "point_b": { "lat": 21.46002, "lon": 95.3884, "name": "Myingyan" }, "ground_truth": { "initial_bearing_deg": 233.52, "cardinal_direction": "SW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Nanmen at (30.96187°, 108.24327°)", " To: Myingyan at (21.46002°, 95.3884°)", "Step 2: Calculate longitude difference", " Δlon = 95.3884 - 108.24327 = -12.8549°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 233.52°", "Step 5: Determine cardinal direction", " 233.5° → SW", "FINAL ANSWER: 233.52° (SW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 10.31028, "lon": 123.94944, "name": "Lapu-Lapu City" }, "point_b": { "lat": -0.41611, "lon": 31.40806, "name": "Lwengo" }, "ground_truth": { "initial_bearing_deg": 270.05, "cardinal_direction": "W", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Lapu-Lapu City at (10.31028°, 123.94944°)", " To: Lwengo at (-0.41611°, 31.40806°)", "Step 2: Calculate longitude difference", " Δlon = 31.40806 - 123.94944 = -92.5414°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 270.05°", "Step 5: Determine cardinal direction", " 270.1° → W", "FINAL ANSWER: 270.05° (W)" ] }, { "task": "bearing_computation", "point_a": { "lat": 18.91614, "lon": -103.87713, "name": "Tecomán" }, "point_b": { "lat": -36.99282, "lon": 174.87986, "name": "Manukau City" }, "ground_truth": { "initial_bearing_deg": 232.37, "cardinal_direction": "SW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Tecomán at (18.91614°, -103.87713°)", " To: Manukau City at (-36.99282°, 174.87986°)", "Step 2: Calculate longitude difference", " Δlon = 174.87986 - -103.87713 = 278.7570°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 232.37°", "Step 5: Determine cardinal direction", " 232.4° → SW", "FINAL ANSWER: 232.37° (SW)" ] }, { "task": "bearing_computation", "point_a": { "lat": -17.345, "lon": -44.94194, "name": "Pirapora" }, "point_b": { "lat": 4.29005, "lon": -74.81612, "name": "Flandes" }, "ground_truth": { "initial_bearing_deg": 303.53, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Pirapora at (-17.345°, -44.94194°)", " To: Flandes at (4.29005°, -74.81612°)", "Step 2: Calculate longitude difference", " Δlon = -74.81612 - -44.94194 = -29.8742°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 303.53°", "Step 5: Determine cardinal direction", " 303.5° → NW", "FINAL ANSWER: 303.53° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 43.50092, "lon": -70.44283, "name": "Saco" }, "point_b": { "lat": 11.22191, "lon": -4.64423, "name": "Karankasso" }, "ground_truth": { "initial_bearing_deg": 98.62, "cardinal_direction": "E", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Saco at (43.50092°, -70.44283°)", " To: Karankasso at (11.22191°, -4.64423°)", "Step 2: Calculate longitude difference", " Δlon = -4.64423 - -70.44283 = 65.7986°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 98.62°", "Step 5: Determine cardinal direction", " 98.6° → E", "FINAL ANSWER: 98.62° (E)" ] }, { "task": "bearing_computation", "point_a": { "lat": -33.30422, "lon": 26.53276, "name": "Grahamstown" }, "point_b": { "lat": 7.6685, "lon": 5.12627, "name": "Igede-Ekiti" }, "ground_truth": { "initial_bearing_deg": 329.67, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Grahamstown at (-33.30422°, 26.53276°)", " To: Igede-Ekiti at (7.6685°, 5.12627°)", "Step 2: Calculate longitude difference", " Δlon = 5.12627 - 26.53276 = -21.4065°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 329.67°", "Step 5: Determine cardinal direction", " 329.7° → NW", "FINAL ANSWER: 329.67° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 47.05893, "lon": -0.87974, "name": "Cholet" }, "point_b": { "lat": -19.93167, "lon": -44.05361, "name": "Contagem" }, "ground_truth": { "initial_bearing_deg": 221.22, "cardinal_direction": "SW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Cholet at (47.05893°, -0.87974°)", " To: Contagem at (-19.93167°, -44.05361°)", "Step 2: Calculate longitude difference", " Δlon = -44.05361 - -0.87974 = -43.1739°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 221.22°", "Step 5: Determine cardinal direction", " 221.2° → SW", "FINAL ANSWER: 221.22° (SW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 35.65087, "lon": 139.79163, "name": "Toyosu" }, "point_b": { "lat": 38.67727, "lon": -87.52863, "name": "Vincennes" }, "ground_truth": { "initial_bearing_deg": 35.11, "cardinal_direction": "NE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Toyosu at (35.65087°, 139.79163°)", " To: Vincennes at (38.67727°, -87.52863°)", "Step 2: Calculate longitude difference", " Δlon = -87.52863 - 139.79163 = -227.3203°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 35.11°", "Step 5: Determine cardinal direction", " 35.1° → NE", "FINAL ANSWER: 35.11° (NE)" ] }, { "task": "bearing_computation", "point_a": { "lat": -13.08333, "lon": 48.85, "name": "Antsohimbondrona" }, "point_b": { "lat": -30.60106, "lon": -71.19901, "name": "Ovalle" }, "ground_truth": { "initial_bearing_deg": 231.46, "cardinal_direction": "SW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Antsohimbondrona at (-13.08333°, 48.85°)", " To: Ovalle at (-30.60106°, -71.19901°)", "Step 2: Calculate longitude difference", " Δlon = -71.19901 - 48.85 = -120.0490°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 231.46°", "Step 5: Determine cardinal direction", " 231.5° → SW", "FINAL ANSWER: 231.46° (SW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 35.818, "lon": 139.368, "name": "Iruma" }, "point_b": { "lat": 9.45149, "lon": 18.94493, "name": "Kyabé" }, "ground_truth": { "initial_bearing_deg": 296.57, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Iruma at (35.818°, 139.368°)", " To: Kyabé at (9.45149°, 18.94493°)", "Step 2: Calculate longitude difference", " Δlon = 18.94493 - 139.368 = -120.4231°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 296.57°", "Step 5: Determine cardinal direction", " 296.6° → NW", "FINAL ANSWER: 296.57° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 42.37649, "lon": -71.23561, "name": "Waltham" }, "point_b": { "lat": -37.73333, "lon": 145.15, "name": "Eltham" }, "ground_truth": { "initial_bearing_deg": 267.2, "cardinal_direction": "W", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Waltham at (42.37649°, -71.23561°)", " To: Eltham at (-37.73333°, 145.15°)", "Step 2: Calculate longitude difference", " Δlon = 145.15 - -71.23561 = 216.3856°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 267.20°", "Step 5: Determine cardinal direction", " 267.2° → W", "FINAL ANSWER: 267.20° (W)" ] }, { "task": "bearing_computation", "point_a": { "lat": 53.85713, "lon": -2.16851, "name": "Colne" }, "point_b": { "lat": 38.91667, "lon": 141.13333, "name": "Ichinoseki" }, "ground_truth": { "initial_bearing_deg": 28.01, "cardinal_direction": "NE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Colne at (53.85713°, -2.16851°)", " To: Ichinoseki at (38.91667°, 141.13333°)", "Step 2: Calculate longitude difference", " Δlon = 141.13333 - -2.16851 = 143.3018°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 28.01°", "Step 5: Determine cardinal direction", " 28.0° → NE", "FINAL ANSWER: 28.01° (NE)" ] }, { "task": "bearing_computation", "point_a": { "lat": 31.09311, "lon": 30.31418, "name": "Abū Ḩummuş" }, "point_b": { "lat": -29.57366, "lon": 31.11552, "name": "Tongaat" }, "ground_truth": { "initial_bearing_deg": 179.2, "cardinal_direction": "S", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Abū Ḩummuş at (31.09311°, 30.31418°)", " To: Tongaat at (-29.57366°, 31.11552°)", "Step 2: Calculate longitude difference", " Δlon = 31.11552 - 30.31418 = 0.8013°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 179.20°", "Step 5: Determine cardinal direction", " 179.2° → S", "FINAL ANSWER: 179.20° (S)" ] }, { "task": "bearing_computation", "point_a": { "lat": 12.77972, "lon": 101.64831, "name": "Klaeng" }, "point_b": { "lat": -15.48211, "lon": 28.35099, "name": "Chisankane" }, "ground_truth": { "initial_bearing_deg": 250.79, "cardinal_direction": "W", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Klaeng at (12.77972°, 101.64831°)", " To: Chisankane at (-15.48211°, 28.35099°)", "Step 2: Calculate longitude difference", " Δlon = 28.35099 - 101.64831 = -73.2973°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 250.79°", "Step 5: Determine cardinal direction", " 250.8° → W", "FINAL ANSWER: 250.79° (W)" ] }, { "task": "bearing_computation", "point_a": { "lat": 53.20271, "lon": 5.80973, "name": "Leeuwarden" }, "point_b": { "lat": -4.52483, "lon": 35.3849, "name": "Katesh" }, "ground_truth": { "initial_bearing_deg": 146.43, "cardinal_direction": "SE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Leeuwarden at (53.20271°, 5.80973°)", " To: Katesh at (-4.52483°, 35.3849°)", "Step 2: Calculate longitude difference", " Δlon = 35.3849 - 5.80973 = 29.5752°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 146.43°", "Step 5: Determine cardinal direction", " 146.4° → SE", "FINAL ANSWER: 146.43° (SE)" ] }, { "task": "bearing_computation", "point_a": { "lat": -17.54234, "lon": -65.83472, "name": "Punata" }, "point_b": { "lat": 40.45245, "lon": -3.70763, "name": "Bellas Vistas" }, "ground_truth": { "initial_bearing_deg": 42.82, "cardinal_direction": "NE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Punata at (-17.54234°, -65.83472°)", " To: Bellas Vistas at (40.45245°, -3.70763°)", "Step 2: Calculate longitude difference", " Δlon = -3.70763 - -65.83472 = 62.1271°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 42.82°", "Step 5: Determine cardinal direction", " 42.8° → NE", "FINAL ANSWER: 42.82° (NE)" ] }, { "task": "bearing_computation", "point_a": { "lat": -33.9049, "lon": 151.01996, "name": "Yagoona" }, "point_b": { "lat": 14.33236, "lon": -16.40513, "name": "Fatick" }, "ground_truth": { "initial_bearing_deg": 213.23, "cardinal_direction": "SW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Yagoona at (-33.9049°, 151.01996°)", " To: Fatick at (14.33236°, -16.40513°)", "Step 2: Calculate longitude difference", " Δlon = -16.40513 - 151.01996 = -167.4251°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 213.23°", "Step 5: Determine cardinal direction", " 213.2° → SW", "FINAL ANSWER: 213.23° (SW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 48.6511, "lon": 2.41406, "name": "Ris-Orangis" }, "point_b": { "lat": -25.96222, "lon": 32.45889, "name": "Matola" }, "ground_truth": { "initial_bearing_deg": 152.74, "cardinal_direction": "SE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Ris-Orangis at (48.6511°, 2.41406°)", " To: Matola at (-25.96222°, 32.45889°)", "Step 2: Calculate longitude difference", " Δlon = 32.45889 - 2.41406 = 30.0448°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 152.74°", "Step 5: Determine cardinal direction", " 152.7° → SE", "FINAL ANSWER: 152.74° (SE)" ] }, { "task": "bearing_computation", "point_a": { "lat": 24.42244, "lon": 88.25238, "name": "Lālgola" }, "point_b": { "lat": -2.5964, "lon": 140.6324, "name": "Abepura" }, "ground_truth": { "initial_bearing_deg": 110.34, "cardinal_direction": "E", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Lālgola at (24.42244°, 88.25238°)", " To: Abepura at (-2.5964°, 140.6324°)", "Step 2: Calculate longitude difference", " Δlon = 140.6324 - 88.25238 = 52.3800°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 110.34°", "Step 5: Determine cardinal direction", " 110.3° → E", "FINAL ANSWER: 110.34° (E)" ] }, { "task": "bearing_computation", "point_a": { "lat": -0.24849, "lon": 35.73194, "name": "Molo" }, "point_b": { "lat": -22.67842, "lon": 14.52663, "name": "Swakopmund" }, "ground_truth": { "initial_bearing_deg": 221.16, "cardinal_direction": "SW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Molo at (-0.24849°, 35.73194°)", " To: Swakopmund at (-22.67842°, 14.52663°)", "Step 2: Calculate longitude difference", " Δlon = 14.52663 - 35.73194 = -21.2053°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 221.16°", "Step 5: Determine cardinal direction", " 221.2° → SW", "FINAL ANSWER: 221.16° (SW)" ] }, { "task": "bearing_computation", "point_a": { "lat": -2.85, "lon": 33.08333, "name": "Misungwi" }, "point_b": { "lat": 45.82972, "lon": 20.46528, "name": "Kikinda" }, "ground_truth": { "initial_bearing_deg": 348.53, "cardinal_direction": "N", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Misungwi at (-2.85°, 33.08333°)", " To: Kikinda at (45.82972°, 20.46528°)", "Step 2: Calculate longitude difference", " Δlon = 20.46528 - 33.08333 = -12.6180°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 348.53°", "Step 5: Determine cardinal direction", " 348.5° → N", "FINAL ANSWER: 348.53° (N)" ] }, { "task": "bearing_computation", "point_a": { "lat": 23.6303, "lon": 85.52156, "name": "Rāmgarh" }, "point_b": { "lat": 40.65642, "lon": 17.70814, "name": "San Vito dei Normanni" }, "ground_truth": { "initial_bearing_deg": 304.46, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Rāmgarh at (23.6303°, 85.52156°)", " To: San Vito dei Normanni at (40.65642°, 17.70814°)", "Step 2: Calculate longitude difference", " Δlon = 17.70814 - 85.52156 = -67.8134°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 304.46°", "Step 5: Determine cardinal direction", " 304.5° → NW", "FINAL ANSWER: 304.46° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": -5.22152, "lon": 145.78695, "name": "Madang" }, "point_b": { "lat": 33.19973, "lon": 120.4578, "name": "Dazhong" }, "ground_truth": { "initial_bearing_deg": 329.76, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Madang at (-5.22152°, 145.78695°)", " To: Dazhong at (33.19973°, 120.4578°)", "Step 2: Calculate longitude difference", " Δlon = 120.4578 - 145.78695 = -25.3291°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 329.76°", "Step 5: Determine cardinal direction", " 329.8° → NW", "FINAL ANSWER: 329.76° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 36.64997, "lon": 3.3308, "name": "Khemis el Khechna" }, "point_b": { "lat": 0.55667, "lon": 31.80222, "name": "Kasanda" }, "ground_truth": { "initial_bearing_deg": 137.32, "cardinal_direction": "SE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Khemis el Khechna at (36.64997°, 3.3308°)", " To: Kasanda at (0.55667°, 31.80222°)", "Step 2: Calculate longitude difference", " Δlon = 31.80222 - 3.3308 = 28.4714°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 137.32°", "Step 5: Determine cardinal direction", " 137.3° → SE", "FINAL ANSWER: 137.32° (SE)" ] }, { "task": "bearing_computation", "point_a": { "lat": -26.14095, "lon": 28.15247, "name": "Edenvale" }, "point_b": { "lat": 36.01393, "lon": -5.60695, "name": "Tarifa" }, "ground_truth": { "initial_bearing_deg": 331.39, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Edenvale at (-26.14095°, 28.15247°)", " To: Tarifa at (36.01393°, -5.60695°)", "Step 2: Calculate longitude difference", " Δlon = -5.60695 - 28.15247 = -33.7594°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 331.39°", "Step 5: Determine cardinal direction", " 331.4° → NW", "FINAL ANSWER: 331.39° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 28.3091, "lon": 70.12652, "name": "Saddiqabad" }, "point_b": { "lat": 29.41369, "lon": 112.16435, "name": "Shenliu" }, "ground_truth": { "initial_bearing_deg": 77.85, "cardinal_direction": "E", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Saddiqabad at (28.3091°, 70.12652°)", " To: Shenliu at (29.41369°, 112.16435°)", "Step 2: Calculate longitude difference", " Δlon = 112.16435 - 70.12652 = 42.0378°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 77.85°", "Step 5: Determine cardinal direction", " 77.8° → E", "FINAL ANSWER: 77.85° (E)" ] }, { "task": "bearing_computation", "point_a": { "lat": 50.50301, "lon": 13.63617, "name": "Most" }, "point_b": { "lat": 19.30023, "lon": 73.05881, "name": "Bhiwandi" }, "ground_truth": { "initial_bearing_deg": 101.16, "cardinal_direction": "E", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Most at (50.50301°, 13.63617°)", " To: Bhiwandi at (19.30023°, 73.05881°)", "Step 2: Calculate longitude difference", " Δlon = 73.05881 - 13.63617 = 59.4226°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 101.16°", "Step 5: Determine cardinal direction", " 101.2° → E", "FINAL ANSWER: 101.16° (E)" ] }, { "task": "bearing_computation", "point_a": { "lat": 20.4925, "lon": -103.4175, "name": "Lomas del Sur" }, "point_b": { "lat": 42.96336, "lon": -85.66809, "name": "Grand Rapids" }, "ground_truth": { "initial_bearing_deg": 29.49, "cardinal_direction": "NE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Lomas del Sur at (20.4925°, -103.4175°)", " To: Grand Rapids at (42.96336°, -85.66809°)", "Step 2: Calculate longitude difference", " Δlon = -85.66809 - -103.4175 = 17.7494°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 29.49°", "Step 5: Determine cardinal direction", " 29.5° → NE", "FINAL ANSWER: 29.49° (NE)" ] }, { "task": "bearing_computation", "point_a": { "lat": 40.80028, "lon": 19.91667, "name": "Kuçovë" }, "point_b": { "lat": -8.94111, "lon": -72.79167, "name": "Marechal Thaumaturgo" }, "ground_truth": { "initial_bearing_deg": 264.95, "cardinal_direction": "W", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Kuçovë at (40.80028°, 19.91667°)", " To: Marechal Thaumaturgo at (-8.94111°, -72.79167°)", "Step 2: Calculate longitude difference", " Δlon = -72.79167 - 19.91667 = -92.7083°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 264.95°", "Step 5: Determine cardinal direction", " 264.9° → W", "FINAL ANSWER: 264.95° (W)" ] }, { "task": "bearing_computation", "point_a": { "lat": 41.49167, "lon": 20.22194, "name": "Bulqizë" }, "point_b": { "lat": 20.22627, "lon": -103.56981, "name": "Zacoalco de Torres" }, "ground_truth": { "initial_bearing_deg": 307.79, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Bulqizë at (41.49167°, 20.22194°)", " To: Zacoalco de Torres at (20.22627°, -103.56981°)", "Step 2: Calculate longitude difference", " Δlon = -103.56981 - 20.22194 = -123.7918°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 307.79°", "Step 5: Determine cardinal direction", " 307.8° → NW", "FINAL ANSWER: 307.79° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": -25.5036, "lon": -54.65067, "name": "Ciudad del Este" }, "point_b": { "lat": 11.89494, "lon": 75.43959, "name": "Chelora" }, "ground_truth": { "initial_bearing_deg": 96.5, "cardinal_direction": "E", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Ciudad del Este at (-25.5036°, -54.65067°)", " To: Chelora at (11.89494°, 75.43959°)", "Step 2: Calculate longitude difference", " Δlon = 75.43959 - -54.65067 = 130.0903°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 96.50°", "Step 5: Determine cardinal direction", " 96.5° → E", "FINAL ANSWER: 96.50° (E)" ] }, { "task": "bearing_computation", "point_a": { "lat": 35.07465, "lon": -1.22431, "name": "Bensekrane" }, "point_b": { "lat": 47.42346, "lon": -120.31035, "name": "Wenatchee" }, "ground_truth": { "initial_bearing_deg": 323.25, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Bensekrane at (35.07465°, -1.22431°)", " To: Wenatchee at (47.42346°, -120.31035°)", "Step 2: Calculate longitude difference", " Δlon = -120.31035 - -1.22431 = -119.0860°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 323.25°", "Step 5: Determine cardinal direction", " 323.2° → NW", "FINAL ANSWER: 323.25° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 49.48056, "lon": 6.0875, "name": "Dudelange" }, "point_b": { "lat": 46.23175, "lon": 27.66907, "name": "Bârlad" }, "ground_truth": { "initial_bearing_deg": 94.45, "cardinal_direction": "E", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Dudelange at (49.48056°, 6.0875°)", " To: Bârlad at (46.23175°, 27.66907°)", "Step 2: Calculate longitude difference", " Δlon = 27.66907 - 6.0875 = 21.5816°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 94.45°", "Step 5: Determine cardinal direction", " 94.5° → E", "FINAL ANSWER: 94.45° (E)" ] }, { "task": "bearing_computation", "point_a": { "lat": 17.64944, "lon": 95.45705, "name": "Hinthada" }, "point_b": { "lat": -22.94564, "lon": 30.48497, "name": "Thohoyandou" }, "ground_truth": { "initial_bearing_deg": 239.6, "cardinal_direction": "SW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Hinthada at (17.64944°, 95.45705°)", " To: Thohoyandou at (-22.94564°, 30.48497°)", "Step 2: Calculate longitude difference", " Δlon = 30.48497 - 95.45705 = -64.9721°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 239.60°", "Step 5: Determine cardinal direction", " 239.6° → SW", "FINAL ANSWER: 239.60° (SW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 33.72835, "lon": -117.14642, "name": "Menifee" }, "point_b": { "lat": 15.40637, "lon": 79.50702, "name": "Kanigiri U" }, "ground_truth": { "initial_bearing_deg": 339.37, "cardinal_direction": "N", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Menifee at (33.72835°, -117.14642°)", " To: Kanigiri U at (15.40637°, 79.50702°)", "Step 2: Calculate longitude difference", " Δlon = 79.50702 - -117.14642 = 196.6534°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 339.37°", "Step 5: Determine cardinal direction", " 339.4° → N", "FINAL ANSWER: 339.37° (N)" ] }, { "task": "bearing_computation", "point_a": { "lat": 20.67738, "lon": -103.34749, "name": "Guadalajara" }, "point_b": { "lat": -33.8406, "lon": 151.00748, "name": "Granville" }, "ground_truth": { "initial_bearing_deg": 241.08, "cardinal_direction": "SW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Guadalajara at (20.67738°, -103.34749°)", " To: Granville at (-33.8406°, 151.00748°)", "Step 2: Calculate longitude difference", " Δlon = 151.00748 - -103.34749 = 254.3550°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 241.08°", "Step 5: Determine cardinal direction", " 241.1° → SW", "FINAL ANSWER: 241.08° (SW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 40.31412, "lon": -112.00688, "name": "Eagle Mountain" }, "point_b": { "lat": 5.31198, "lon": -3.99363, "name": "Marcory" }, "ground_truth": { "initial_bearing_deg": 74.1, "cardinal_direction": "E", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Eagle Mountain at (40.31412°, -112.00688°)", " To: Marcory at (5.31198°, -3.99363°)", "Step 2: Calculate longitude difference", " Δlon = -3.99363 - -112.00688 = 108.0132°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 74.10°", "Step 5: Determine cardinal direction", " 74.1° → E", "FINAL ANSWER: 74.10° (E)" ] }, { "task": "bearing_computation", "point_a": { "lat": 2.7389, "lon": 102.2487, "name": "Kuala Pilah" }, "point_b": { "lat": 1.25881, "lon": 35.09569, "name": "Makutano" }, "ground_truth": { "initial_bearing_deg": 270.21, "cardinal_direction": "W", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Kuala Pilah at (2.7389°, 102.2487°)", " To: Makutano at (1.25881°, 35.09569°)", "Step 2: Calculate longitude difference", " Δlon = 35.09569 - 102.2487 = -67.1530°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 270.21°", "Step 5: Determine cardinal direction", " 270.2° → W", "FINAL ANSWER: 270.21° (W)" ] }, { "task": "bearing_computation", "point_a": { "lat": -8.39818, "lon": -74.53774, "name": "San Fernando" }, "point_b": { "lat": 45.25167, "lon": 19.83694, "name": "Novi Sad" }, "ground_truth": { "initial_bearing_deg": 45.3, "cardinal_direction": "NE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: San Fernando at (-8.39818°, -74.53774°)", " To: Novi Sad at (45.25167°, 19.83694°)", "Step 2: Calculate longitude difference", " Δlon = 19.83694 - -74.53774 = 94.3747°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 45.30°", "Step 5: Determine cardinal direction", " 45.3° → NE", "FINAL ANSWER: 45.30° (NE)" ] }, { "task": "bearing_computation", "point_a": { "lat": 7.50077, "lon": 134.6238, "name": "Ngerulmud" }, "point_b": { "lat": -27.00805, "lon": 27.3646, "name": "Vredefort" }, "ground_truth": { "initial_bearing_deg": 243.96, "cardinal_direction": "SW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Ngerulmud at (7.50077°, 134.6238°)", " To: Vredefort at (-27.00805°, 27.3646°)", "Step 2: Calculate longitude difference", " Δlon = 27.3646 - 134.6238 = -107.2592°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 243.96°", "Step 5: Determine cardinal direction", " 244.0° → SW", "FINAL ANSWER: 243.96° (SW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 9.36238, "lon": -73.60313, "name": "Chiriguaná" }, "point_b": { "lat": 4.95384, "lon": -6.08531, "name": "Sassandra" }, "ground_truth": { "initial_bearing_deg": 88.55, "cardinal_direction": "E", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Chiriguaná at (9.36238°, -73.60313°)", " To: Sassandra at (4.95384°, -6.08531°)", "Step 2: Calculate longitude difference", " Δlon = -6.08531 - -73.60313 = 67.5178°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 88.55°", "Step 5: Determine cardinal direction", " 88.5° → E", "FINAL ANSWER: 88.55° (E)" ] }, { "task": "bearing_computation", "point_a": { "lat": 38.76511, "lon": -76.89831, "name": "Clinton" }, "point_b": { "lat": 36.52056, "lon": 6.26111, "name": "Sidi Mérouane" }, "ground_truth": { "initial_bearing_deg": 63.14, "cardinal_direction": "NE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Clinton at (38.76511°, -76.89831°)", " To: Sidi Mérouane at (36.52056°, 6.26111°)", "Step 2: Calculate longitude difference", " Δlon = 6.26111 - -76.89831 = 83.1594°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 63.14°", "Step 5: Determine cardinal direction", " 63.1° → NE", "FINAL ANSWER: 63.14° (NE)" ] }, { "task": "bearing_computation", "point_a": { "lat": 14.87964, "lon": -91.45699, "name": "Salcajá" }, "point_b": { "lat": 33.88474, "lon": -118.41091, "name": "Manhattan Beach" }, "ground_truth": { "initial_bearing_deg": 312.83, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Salcajá at (14.87964°, -91.45699°)", " To: Manhattan Beach at (33.88474°, -118.41091°)", "Step 2: Calculate longitude difference", " Δlon = -118.41091 - -91.45699 = -26.9539°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 312.83°", "Step 5: Determine cardinal direction", " 312.8° → NW", "FINAL ANSWER: 312.83° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 18.54478, "lon": -72.30036, "name": "Delmas" }, "point_b": { "lat": -21.03306, "lon": -44.75806, "name": "Bom Sucesso" }, "ground_truth": { "initial_bearing_deg": 144.43, "cardinal_direction": "SE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Delmas at (18.54478°, -72.30036°)", " To: Bom Sucesso at (-21.03306°, -44.75806°)", "Step 2: Calculate longitude difference", " Δlon = -44.75806 - -72.30036 = 27.5423°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 144.43°", "Step 5: Determine cardinal direction", " 144.4° → SE", "FINAL ANSWER: 144.43° (SE)" ] }, { "task": "bearing_computation", "point_a": { "lat": 38.67351, "lon": 29.4058, "name": "Uşak" }, "point_b": { "lat": -26.31401, "lon": 26.82223, "name": "Ventersdorp" }, "ground_truth": { "initial_bearing_deg": 182.55, "cardinal_direction": "S", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Uşak at (38.67351°, 29.4058°)", " To: Ventersdorp at (-26.31401°, 26.82223°)", "Step 2: Calculate longitude difference", " Δlon = 26.82223 - 29.4058 = -2.5836°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 182.55°", "Step 5: Determine cardinal direction", " 182.6° → S", "FINAL ANSWER: 182.55° (S)" ] }, { "task": "bearing_computation", "point_a": { "lat": -17.73111, "lon": -49.09944, "name": "Morrinhos" }, "point_b": { "lat": -27.31472, "lon": -48.55917, "name": "Governador Celso Ramos" }, "ground_truth": { "initial_bearing_deg": 177.12, "cardinal_direction": "S", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Morrinhos at (-17.73111°, -49.09944°)", " To: Governador Celso Ramos at (-27.31472°, -48.55917°)", "Step 2: Calculate longitude difference", " Δlon = -48.55917 - -49.09944 = 0.5403°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 177.12°", "Step 5: Determine cardinal direction", " 177.1° → S", "FINAL ANSWER: 177.12° (S)" ] }, { "task": "bearing_computation", "point_a": { "lat": -7.31056, "lon": -50.04833, "name": "Rio Maria" }, "point_b": { "lat": 14.79032, "lon": -15.90803, "name": "Mbaké" }, "ground_truth": { "initial_bearing_deg": 56.8, "cardinal_direction": "NE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Rio Maria at (-7.31056°, -50.04833°)", " To: Mbaké at (14.79032°, -15.90803°)", "Step 2: Calculate longitude difference", " Δlon = -15.90803 - -50.04833 = 34.1403°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 56.80°", "Step 5: Determine cardinal direction", " 56.8° → NE", "FINAL ANSWER: 56.80° (NE)" ] }, { "task": "bearing_computation", "point_a": { "lat": -3.52278, "lon": -40.34278, "name": "Massapê" }, "point_b": { "lat": 5.55221, "lon": -0.33912, "name": "Mandela" }, "ground_truth": { "initial_bearing_deg": 77.37, "cardinal_direction": "E", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Massapê at (-3.52278°, -40.34278°)", " To: Mandela at (5.55221°, -0.33912°)", "Step 2: Calculate longitude difference", " Δlon = -0.33912 - -40.34278 = 40.0037°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 77.37°", "Step 5: Determine cardinal direction", " 77.4° → E", "FINAL ANSWER: 77.37° (E)" ] }, { "task": "bearing_computation", "point_a": { "lat": 44.9483, "lon": -93.34801, "name": "Saint Louis Park" }, "point_b": { "lat": 54.90973, "lon": 64.4319, "name": "Kurtamysh" }, "ground_truth": { "initial_bearing_deg": 12.82, "cardinal_direction": "N", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Saint Louis Park at (44.9483°, -93.34801°)", " To: Kurtamysh at (54.90973°, 64.4319°)", "Step 2: Calculate longitude difference", " Δlon = 64.4319 - -93.34801 = 157.7799°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 12.82°", "Step 5: Determine cardinal direction", " 12.8° → N", "FINAL ANSWER: 12.82° (N)" ] }, { "task": "bearing_computation", "point_a": { "lat": -33.01529, "lon": 27.91162, "name": "East London" }, "point_b": { "lat": 43.67159, "lon": -79.404, "name": "Annex" }, "ground_truth": { "initial_bearing_deg": 303.77, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: East London at (-33.01529°, 27.91162°)", " To: Annex at (43.67159°, -79.404°)", "Step 2: Calculate longitude difference", " Δlon = -79.404 - 27.91162 = -107.3156°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 303.77°", "Step 5: Determine cardinal direction", " 303.8° → NW", "FINAL ANSWER: 303.77° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 14.2, "lon": 24.66667, "name": "Kutum" }, "point_b": { "lat": 51.66361, "lon": 16.0845, "name": "Głogów" }, "ground_truth": { "initial_bearing_deg": 351.37, "cardinal_direction": "N", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Kutum at (14.2°, 24.66667°)", " To: Głogów at (51.66361°, 16.0845°)", "Step 2: Calculate longitude difference", " Δlon = 16.0845 - 24.66667 = -8.5822°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 351.37°", "Step 5: Determine cardinal direction", " 351.4° → N", "FINAL ANSWER: 351.37° (N)" ] }, { "task": "bearing_computation", "point_a": { "lat": 54.61378, "lon": 25.95537, "name": "Astraviec" }, "point_b": { "lat": 43.6475, "lon": 111.97667, "name": "Erenhot" }, "ground_truth": { "initial_bearing_deg": 63.57, "cardinal_direction": "NE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Astraviec at (54.61378°, 25.95537°)", " To: Erenhot at (43.6475°, 111.97667°)", "Step 2: Calculate longitude difference", " Δlon = 111.97667 - 25.95537 = 86.0213°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 63.57°", "Step 5: Determine cardinal direction", " 63.6° → NE", "FINAL ANSWER: 63.57° (NE)" ] }, { "task": "bearing_computation", "point_a": { "lat": 33.88168, "lon": -118.11701, "name": "Bellflower" }, "point_b": { "lat": -7.5817, "lon": -39.28348, "name": "Jardim" }, "ground_truth": { "initial_bearing_deg": 102.55, "cardinal_direction": "E", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Bellflower at (33.88168°, -118.11701°)", " To: Jardim at (-7.5817°, -39.28348°)", "Step 2: Calculate longitude difference", " Δlon = -39.28348 - -118.11701 = 78.8335°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 102.55°", "Step 5: Determine cardinal direction", " 102.5° → E", "FINAL ANSWER: 102.55° (E)" ] }, { "task": "bearing_computation", "point_a": { "lat": 48.59479, "lon": 17.82591, "name": "Piešťany" }, "point_b": { "lat": 9.91861, "lon": -68.30472, "name": "Tinaquillo" }, "ground_truth": { "initial_bearing_deg": 273.73, "cardinal_direction": "W", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Piešťany at (48.59479°, 17.82591°)", " To: Tinaquillo at (9.91861°, -68.30472°)", "Step 2: Calculate longitude difference", " Δlon = -68.30472 - 17.82591 = -86.1306°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 273.73°", "Step 5: Determine cardinal direction", " 273.7° → W", "FINAL ANSWER: 273.73° (W)" ] }, { "task": "bearing_computation", "point_a": { "lat": -7.96556, "lon": 110.60361, "name": "Wonosari" }, "point_b": { "lat": 46.56718, "lon": 26.91384, "name": "Bacău" }, "ground_truth": { "initial_bearing_deg": 316.88, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Wonosari at (-7.96556°, 110.60361°)", " To: Bacău at (46.56718°, 26.91384°)", "Step 2: Calculate longitude difference", " Δlon = 26.91384 - 110.60361 = -83.6898°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 316.88°", "Step 5: Determine cardinal direction", " 316.9° → NW", "FINAL ANSWER: 316.88° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 10.1664, "lon": 76.20179, "name": "Vadakakarai" }, "point_b": { "lat": 9.03333, "lon": 38.15, "name": "Gīnch’ī" }, "ground_truth": { "initial_bearing_deg": 271.63, "cardinal_direction": "W", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Vadakakarai at (10.1664°, 76.20179°)", " To: Gīnch’ī at (9.03333°, 38.15°)", "Step 2: Calculate longitude difference", " Δlon = 38.15 - 76.20179 = -38.0518°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 271.63°", "Step 5: Determine cardinal direction", " 271.6° → W", "FINAL ANSWER: 271.63° (W)" ] }, { "task": "bearing_computation", "point_a": { "lat": 46.25773, "lon": 126.28065, "name": "Lanxi" }, "point_b": { "lat": -14.33611, "lon": -43.77361, "name": "Malhada" }, "ground_truth": { "initial_bearing_deg": 342.1, "cardinal_direction": "N", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Lanxi at (46.25773°, 126.28065°)", " To: Malhada at (-14.33611°, -43.77361°)", "Step 2: Calculate longitude difference", " Δlon = -43.77361 - 126.28065 = -170.0543°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 342.10°", "Step 5: Determine cardinal direction", " 342.1° → N", "FINAL ANSWER: 342.10° (N)" ] }, { "task": "bearing_computation", "point_a": { "lat": 50.70825, "lon": -120.41337, "name": "Brocklehurst" }, "point_b": { "lat": 34.1463, "lon": 73.21168, "name": "Abbottabad" }, "ground_truth": { "initial_bearing_deg": 348.73, "cardinal_direction": "N", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Brocklehurst at (50.70825°, -120.41337°)", " To: Abbottabad at (34.1463°, 73.21168°)", "Step 2: Calculate longitude difference", " Δlon = 73.21168 - -120.41337 = 193.6250°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 348.73°", "Step 5: Determine cardinal direction", " 348.7° → N", "FINAL ANSWER: 348.73° (N)" ] }, { "task": "bearing_computation", "point_a": { "lat": 34.01325, "lon": -6.83255, "name": "Rabat" }, "point_b": { "lat": 29.70885, "lon": 73.62539, "name": "Padampur" }, "ground_truth": { "initial_bearing_deg": 68.91, "cardinal_direction": "E", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Rabat at (34.01325°, -6.83255°)", " To: Padampur at (29.70885°, 73.62539°)", "Step 2: Calculate longitude difference", " Δlon = 73.62539 - -6.83255 = 80.4579°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 68.91°", "Step 5: Determine cardinal direction", " 68.9° → E", "FINAL ANSWER: 68.91° (E)" ] }, { "task": "bearing_computation", "point_a": { "lat": 13.2045, "lon": 108.21029, "name": "Ea Drăng" }, "point_b": { "lat": 7.4839, "lon": 80.3683, "name": "Kurunegala" }, "ground_truth": { "initial_bearing_deg": 260.99, "cardinal_direction": "W", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Ea Drăng at (13.2045°, 108.21029°)", " To: Kurunegala at (7.4839°, 80.3683°)", "Step 2: Calculate longitude difference", " Δlon = 80.3683 - 108.21029 = -27.8420°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 260.99°", "Step 5: Determine cardinal direction", " 261.0° → W", "FINAL ANSWER: 260.99° (W)" ] }, { "task": "bearing_computation", "point_a": { "lat": -4.36667, "lon": 35.08333, "name": "Basotu" }, "point_b": { "lat": 41.52614, "lon": -87.88922, "name": "Mokena" }, "ground_truth": { "initial_bearing_deg": 315.09, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Basotu at (-4.36667°, 35.08333°)", " To: Mokena at (41.52614°, -87.88922°)", "Step 2: Calculate longitude difference", " Δlon = -87.88922 - 35.08333 = -122.9725°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 315.09°", "Step 5: Determine cardinal direction", " 315.1° → NW", "FINAL ANSWER: 315.09° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 28.01888, "lon": -82.11469, "name": "Plant City" }, "point_b": { "lat": -37.84205, "lon": 145.0694, "name": "Camberwell" }, "ground_truth": { "initial_bearing_deg": 243.45, "cardinal_direction": "SW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Plant City at (28.01888°, -82.11469°)", " To: Camberwell at (-37.84205°, 145.0694°)", "Step 2: Calculate longitude difference", " Δlon = 145.0694 - -82.11469 = 227.1841°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 243.45°", "Step 5: Determine cardinal direction", " 243.4° → SW", "FINAL ANSWER: 243.45° (SW)" ] }, { "task": "bearing_computation", "point_a": { "lat": -17.82772, "lon": 31.05337, "name": "Harare" }, "point_b": { "lat": -22.66167, "lon": -50.41222, "name": "Assis" }, "ground_truth": { "initial_bearing_deg": 250.41, "cardinal_direction": "W", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Harare at (-17.82772°, 31.05337°)", " To: Assis at (-22.66167°, -50.41222°)", "Step 2: Calculate longitude difference", " Δlon = -50.41222 - 31.05337 = -81.4656°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 250.41°", "Step 5: Determine cardinal direction", " 250.4° → W", "FINAL ANSWER: 250.41° (W)" ] }, { "task": "bearing_computation", "point_a": { "lat": 30.73058, "lon": 76.69368, "name": "Balaungi" }, "point_b": { "lat": 30.21754, "lon": 105.7452, "name": "Shuangjiang" }, "ground_truth": { "initial_bearing_deg": 83.66, "cardinal_direction": "E", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Balaungi at (30.73058°, 76.69368°)", " To: Shuangjiang at (30.21754°, 105.7452°)", "Step 2: Calculate longitude difference", " Δlon = 105.7452 - 76.69368 = 29.0515°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 83.66°", "Step 5: Determine cardinal direction", " 83.7° → E", "FINAL ANSWER: 83.66° (E)" ] }, { "task": "bearing_computation", "point_a": { "lat": -25.40222, "lon": 32.80722, "name": "Manhiça" }, "point_b": { "lat": 36.18683, "lon": 5.31347, "name": "Aïn Arnat" }, "ground_truth": { "initial_bearing_deg": 336.09, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Manhiça at (-25.40222°, 32.80722°)", " To: Aïn Arnat at (36.18683°, 5.31347°)", "Step 2: Calculate longitude difference", " Δlon = 5.31347 - 32.80722 = -27.4938°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 336.09°", "Step 5: Determine cardinal direction", " 336.1° → NW", "FINAL ANSWER: 336.09° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": -7.86139, "lon": -38.75972, "name": "São José do Belmonte" }, "point_b": { "lat": 29.16042, "lon": 78.00762, "name": "Hastināpur" }, "ground_truth": { "initial_bearing_deg": 61.19, "cardinal_direction": "NE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: São José do Belmonte at (-7.86139°, -38.75972°)", " To: Hastināpur at (29.16042°, 78.00762°)", "Step 2: Calculate longitude difference", " Δlon = 78.00762 - -38.75972 = 116.7673°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 61.19°", "Step 5: Determine cardinal direction", " 61.2° → NE", "FINAL ANSWER: 61.19° (NE)" ] }, { "task": "bearing_computation", "point_a": { "lat": 35.49474, "lon": 6.92492, "name": "Kaïs" }, "point_b": { "lat": 16.6614, "lon": -9.6149, "name": "Ayoun El Atrous" }, "ground_truth": { "initial_bearing_deg": 222.29, "cardinal_direction": "SW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Kaïs at (35.49474°, 6.92492°)", " To: Ayoun El Atrous at (16.6614°, -9.6149°)", "Step 2: Calculate longitude difference", " Δlon = -9.6149 - 6.92492 = -16.5398°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 222.29°", "Step 5: Determine cardinal direction", " 222.3° → SW", "FINAL ANSWER: 222.29° (SW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 48.44963, "lon": -123.50261, "name": "Langford" }, "point_b": { "lat": 6.56913, "lon": -8.00253, "name": "Bloléquin" }, "ground_truth": { "initial_bearing_deg": 66.17, "cardinal_direction": "NE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Langford at (48.44963°, -123.50261°)", " To: Bloléquin at (6.56913°, -8.00253°)", "Step 2: Calculate longitude difference", " Δlon = -8.00253 - -123.50261 = 115.5001°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 66.17°", "Step 5: Determine cardinal direction", " 66.2° → NE", "FINAL ANSWER: 66.17° (NE)" ] }, { "task": "bearing_computation", "point_a": { "lat": 10.86242, "lon": 76.09218, "name": "Irimbiliyam" }, "point_b": { "lat": 22.91, "lon": -81.85639, "name": "Madruga" }, "ground_truth": { "initial_bearing_deg": 327.52, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Irimbiliyam at (10.86242°, 76.09218°)", " To: Madruga at (22.91°, -81.85639°)", "Step 2: Calculate longitude difference", " Δlon = -81.85639 - 76.09218 = -157.9486°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 327.52°", "Step 5: Determine cardinal direction", " 327.5° → NW", "FINAL ANSWER: 327.52° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 5.7, "lon": 101.83333, "name": "Kampung Jeli" }, "point_b": { "lat": 40.70788, "lon": -73.7868, "name": "Hillside" }, "ground_truth": { "initial_bearing_deg": 355.43, "cardinal_direction": "N", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Kampung Jeli at (5.7°, 101.83333°)", " To: Hillside at (40.70788°, -73.7868°)", "Step 2: Calculate longitude difference", " Δlon = -73.7868 - 101.83333 = -175.6201°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 355.43°", "Step 5: Determine cardinal direction", " 355.4° → N", "FINAL ANSWER: 355.43° (N)" ] }, { "task": "bearing_computation", "point_a": { "lat": 11.17151, "lon": 75.80611, "name": "Beypore" }, "point_b": { "lat": 51.10821, "lon": 6.94831, "name": "Langenfeld" }, "ground_truth": { "initial_bearing_deg": 320.87, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Beypore at (11.17151°, 75.80611°)", " To: Langenfeld at (51.10821°, 6.94831°)", "Step 2: Calculate longitude difference", " Δlon = 6.94831 - 75.80611 = -68.8578°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 320.87°", "Step 5: Determine cardinal direction", " 320.9° → NW", "FINAL ANSWER: 320.87° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 43.96667, "lon": 116.03333, "name": "Xilin Hot" }, "point_b": { "lat": -2.51667, "lon": 32.9, "name": "Mwanza" }, "ground_truth": { "initial_bearing_deg": 263.41, "cardinal_direction": "W", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Xilin Hot at (43.96667°, 116.03333°)", " To: Mwanza at (-2.51667°, 32.9°)", "Step 2: Calculate longitude difference", " Δlon = 32.9 - 116.03333 = -83.1333°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 263.41°", "Step 5: Determine cardinal direction", " 263.4° → W", "FINAL ANSWER: 263.41° (W)" ] }, { "task": "bearing_computation", "point_a": { "lat": 40.98333, "lon": 68.9, "name": "Zafar" }, "point_b": { "lat": -23.20083, "lon": -47.28694, "name": "Salto" }, "ground_truth": { "initial_bearing_deg": 267.82, "cardinal_direction": "W", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Zafar at (40.98333°, 68.9°)", " To: Salto at (-23.20083°, -47.28694°)", "Step 2: Calculate longitude difference", " Δlon = -47.28694 - 68.9 = -116.1869°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 267.82°", "Step 5: Determine cardinal direction", " 267.8° → W", "FINAL ANSWER: 267.82° (W)" ] }, { "task": "bearing_computation", "point_a": { "lat": 22.80667, "lon": -80.07556, "name": "Sagua la Grande" }, "point_b": { "lat": 22.61892, "lon": -83.70694, "name": "Viñales" }, "ground_truth": { "initial_bearing_deg": 267.49, "cardinal_direction": "W", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Sagua la Grande at (22.80667°, -80.07556°)", " To: Viñales at (22.61892°, -83.70694°)", "Step 2: Calculate longitude difference", " Δlon = -83.70694 - -80.07556 = -3.6314°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 267.49°", "Step 5: Determine cardinal direction", " 267.5° → W", "FINAL ANSWER: 267.49° (W)" ] }, { "task": "bearing_computation", "point_a": { "lat": 6.26812, "lon": 100.42167, "name": "Jitra" }, "point_b": { "lat": 41.60797, "lon": 2.28773, "name": "Granollers" }, "ground_truth": { "initial_bearing_deg": 312.22, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Jitra at (6.26812°, 100.42167°)", " To: Granollers at (41.60797°, 2.28773°)", "Step 2: Calculate longitude difference", " Δlon = 2.28773 - 100.42167 = -98.1339°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 312.22°", "Step 5: Determine cardinal direction", " 312.2° → NW", "FINAL ANSWER: 312.22° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": -7.18833, "lon": -39.73694, "name": "Santana do Cariri" }, "point_b": { "lat": 4.0913, "lon": 9.3144, "name": "Mutengene" }, "ground_truth": { "initial_bearing_deg": 78.55, "cardinal_direction": "E", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Santana do Cariri at (-7.18833°, -39.73694°)", " To: Mutengene at (4.0913°, 9.3144°)", "Step 2: Calculate longitude difference", " Δlon = 9.3144 - -39.73694 = 49.0513°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 78.55°", "Step 5: Determine cardinal direction", " 78.5° → E", "FINAL ANSWER: 78.55° (E)" ] }, { "task": "bearing_computation", "point_a": { "lat": 47.67399, "lon": -122.12151, "name": "Redmond" }, "point_b": { "lat": 13.44189, "lon": 79.55314, "name": "Puttūr" }, "ground_truth": { "initial_bearing_deg": 336.46, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Redmond at (47.67399°, -122.12151°)", " To: Puttūr at (13.44189°, 79.55314°)", "Step 2: Calculate longitude difference", " Δlon = 79.55314 - -122.12151 = 201.6746°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 336.46°", "Step 5: Determine cardinal direction", " 336.5° → NW", "FINAL ANSWER: 336.46° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 28.0199, "lon": -82.77323, "name": "Dunedin" }, "point_b": { "lat": -23.38032, "lon": 150.50595, "name": "Rockhampton" }, "ground_truth": { "initial_bearing_deg": 262.83, "cardinal_direction": "W", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Dunedin at (28.0199°, -82.77323°)", " To: Rockhampton at (-23.38032°, 150.50595°)", "Step 2: Calculate longitude difference", " Δlon = 150.50595 - -82.77323 = 233.2792°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 262.83°", "Step 5: Determine cardinal direction", " 262.8° → W", "FINAL ANSWER: 262.83° (W)" ] }, { "task": "bearing_computation", "point_a": { "lat": 19.30133, "lon": 76.49735, "name": "Manwath" }, "point_b": { "lat": 55.84244, "lon": 38.19362, "name": "Monino" }, "ground_truth": { "initial_bearing_deg": 331.29, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Manwath at (19.30133°, 76.49735°)", " To: Monino at (55.84244°, 38.19362°)", "Step 2: Calculate longitude difference", " Δlon = 38.19362 - 76.49735 = -38.3037°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 331.29°", "Step 5: Determine cardinal direction", " 331.3° → NW", "FINAL ANSWER: 331.29° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 37.49466, "lon": -120.84659, "name": "Turlock" }, "point_b": { "lat": 22.02074, "lon": 82.5666, "name": "Nailā" }, "ground_truth": { "initial_bearing_deg": 335.69, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Turlock at (37.49466°, -120.84659°)", " To: Nailā at (22.02074°, 82.5666°)", "Step 2: Calculate longitude difference", " Δlon = 82.5666 - -120.84659 = 203.4132°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 335.69°", "Step 5: Determine cardinal direction", " 335.7° → NW", "FINAL ANSWER: 335.69° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 51.7874, "lon": 56.35987, "name": "Saraktash" }, "point_b": { "lat": 10.02798, "lon": 39.8528, "name": "Kobo" }, "ground_truth": { "initial_bearing_deg": 203.81, "cardinal_direction": "SW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Saraktash at (51.7874°, 56.35987°)", " To: Kobo at (10.02798°, 39.8528°)", "Step 2: Calculate longitude difference", " Δlon = 39.8528 - 56.35987 = -16.5071°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 203.81°", "Step 5: Determine cardinal direction", " 203.8° → SW", "FINAL ANSWER: 203.81° (SW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 42.96336, "lon": -85.66809, "name": "Grand Rapids" }, "point_b": { "lat": -27.58333, "lon": 153.1, "name": "Eight Mile Plains" }, "ground_truth": { "initial_bearing_deg": 268.06, "cardinal_direction": "W", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Grand Rapids at (42.96336°, -85.66809°)", " To: Eight Mile Plains at (-27.58333°, 153.1°)", "Step 2: Calculate longitude difference", " Δlon = 153.1 - -85.66809 = 238.7681°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 268.06°", "Step 5: Determine cardinal direction", " 268.1° → W", "FINAL ANSWER: 268.06° (W)" ] }, { "task": "bearing_computation", "point_a": { "lat": -9.40611, "lon": -38.21472, "name": "Paulo Afonso" }, "point_b": { "lat": 35.83333, "lon": 140.23333, "name": "Ajiki" }, "ground_truth": { "initial_bearing_deg": 2.82, "cardinal_direction": "N", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Paulo Afonso at (-9.40611°, -38.21472°)", " To: Ajiki at (35.83333°, 140.23333°)", "Step 2: Calculate longitude difference", " Δlon = 140.23333 - -38.21472 = 178.4480°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 2.82°", "Step 5: Determine cardinal direction", " 2.8° → N", "FINAL ANSWER: 2.82° (N)" ] }, { "task": "bearing_computation", "point_a": { "lat": 50.04862, "lon": 14.5244, "name": "Hostivař" }, "point_b": { "lat": -25.9957, "lon": 28.1971, "name": "Ivory Park" }, "ground_truth": { "initial_bearing_deg": 167.41, "cardinal_direction": "S", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Hostivař at (50.04862°, 14.5244°)", " To: Ivory Park at (-25.9957°, 28.1971°)", "Step 2: Calculate longitude difference", " Δlon = 28.1971 - 14.5244 = 13.6727°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 167.41°", "Step 5: Determine cardinal direction", " 167.4° → S", "FINAL ANSWER: 167.41° (S)" ] }, { "task": "bearing_computation", "point_a": { "lat": 47.76977, "lon": 9.17136, "name": "Überlingen" }, "point_b": { "lat": 47.23088, "lon": 16.62155, "name": "Szombathely" }, "ground_truth": { "initial_bearing_deg": 93.35, "cardinal_direction": "E", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Überlingen at (47.76977°, 9.17136°)", " To: Szombathely at (47.23088°, 16.62155°)", "Step 2: Calculate longitude difference", " Δlon = 16.62155 - 9.17136 = 7.4502°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 93.35°", "Step 5: Determine cardinal direction", " 93.3° → E", "FINAL ANSWER: 93.35° (E)" ] }, { "task": "bearing_computation", "point_a": { "lat": 51.61379, "lon": 7.19738, "name": "Recklinghausen" }, "point_b": { "lat": -27.64613, "lon": 152.85965, "name": "Redbank Plains" }, "ground_truth": { "initial_bearing_deg": 60.28, "cardinal_direction": "NE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Recklinghausen at (51.61379°, 7.19738°)", " To: Redbank Plains at (-27.64613°, 152.85965°)", "Step 2: Calculate longitude difference", " Δlon = 152.85965 - 7.19738 = 145.6623°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 60.28°", "Step 5: Determine cardinal direction", " 60.3° → NE", "FINAL ANSWER: 60.28° (NE)" ] }, { "task": "bearing_computation", "point_a": { "lat": 44.35012, "lon": -78.73286, "name": "Lindsay" }, "point_b": { "lat": 24.33353, "lon": 93.66999, "name": "Churāchāndpur" }, "ground_truth": { "initial_bearing_deg": 7.41, "cardinal_direction": "N", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Lindsay at (44.35012°, -78.73286°)", " To: Churāchāndpur at (24.33353°, 93.66999°)", "Step 2: Calculate longitude difference", " Δlon = 93.66999 - -78.73286 = 172.4029°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 7.41°", "Step 5: Determine cardinal direction", " 7.4° → N", "FINAL ANSWER: 7.41° (N)" ] }, { "task": "bearing_computation", "point_a": { "lat": 42.00288, "lon": -71.51478, "name": "Woonsocket" }, "point_b": { "lat": 27.59441, "lon": 94.72402, "name": "Silapathar" }, "ground_truth": { "initial_bearing_deg": 12.9, "cardinal_direction": "N", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Woonsocket at (42.00288°, -71.51478°)", " To: Silapathar at (27.59441°, 94.72402°)", "Step 2: Calculate longitude difference", " Δlon = 94.72402 - -71.51478 = 166.2388°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 12.90°", "Step 5: Determine cardinal direction", " 12.9° → N", "FINAL ANSWER: 12.90° (N)" ] }, { "task": "bearing_computation", "point_a": { "lat": 36.77667, "lon": 121.15972, "name": "Dongcun" }, "point_b": { "lat": -9.13333, "lon": -35.74833, "name": "Joaquim Gomes" }, "ground_truth": { "initial_bearing_deg": 317.09, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Dongcun at (36.77667°, 121.15972°)", " To: Joaquim Gomes at (-9.13333°, -35.74833°)", "Step 2: Calculate longitude difference", " Δlon = -35.74833 - 121.15972 = -156.9081°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 317.09°", "Step 5: Determine cardinal direction", " 317.1° → NW", "FINAL ANSWER: 317.09° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 13.73939, "lon": 106.98727, "name": "Banlung" }, "point_b": { "lat": 51.44657, "lon": 0.21423, "name": "Dartford" }, "ground_truth": { "initial_bearing_deg": 323.36, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Banlung at (13.73939°, 106.98727°)", " To: Dartford at (51.44657°, 0.21423°)", "Step 2: Calculate longitude difference", " Δlon = 0.21423 - 106.98727 = -106.7730°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 323.36°", "Step 5: Determine cardinal direction", " 323.4° → NW", "FINAL ANSWER: 323.36° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 31.54514, "lon": 73.82891, "name": "Chak Five Hundred Seventy-five" }, "point_b": { "lat": 48.44248, "lon": 22.718, "name": "Mukachevo" }, "ground_truth": { "initial_bearing_deg": 309.11, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Chak Five Hundred Seventy-five at (31.54514°, 73.82891°)", " To: Mukachevo at (48.44248°, 22.718°)", "Step 2: Calculate longitude difference", " Δlon = 22.718 - 73.82891 = -51.1109°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 309.11°", "Step 5: Determine cardinal direction", " 309.1° → NW", "FINAL ANSWER: 309.11° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": -12.78234, "lon": 45.22878, "name": "Mamoudzou" }, "point_b": { "lat": 43.93064, "lon": 10.92365, "name": "Pistoia" }, "ground_truth": { "initial_bearing_deg": 333.33, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Mamoudzou at (-12.78234°, 45.22878°)", " To: Pistoia at (43.93064°, 10.92365°)", "Step 2: Calculate longitude difference", " Δlon = 10.92365 - 45.22878 = -34.3051°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 333.33°", "Step 5: Determine cardinal direction", " 333.3° → NW", "FINAL ANSWER: 333.33° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 51.78826, "lon": 6.13865, "name": "Kleve" }, "point_b": { "lat": 54.42119, "lon": 86.29907, "name": "Belovo" }, "ground_truth": { "initial_bearing_deg": 53.45, "cardinal_direction": "NE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Kleve at (51.78826°, 6.13865°)", " To: Belovo at (54.42119°, 86.29907°)", "Step 2: Calculate longitude difference", " Δlon = 86.29907 - 6.13865 = 80.1604°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 53.45°", "Step 5: Determine cardinal direction", " 53.5° → NE", "FINAL ANSWER: 53.45° (NE)" ] }, { "task": "bearing_computation", "point_a": { "lat": 46.05007, "lon": -71.96579, "name": "Victoriaville" }, "point_b": { "lat": 32.55556, "lon": 35.85, "name": "Irbid" }, "ground_truth": { "initial_bearing_deg": 55.13, "cardinal_direction": "NE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Victoriaville at (46.05007°, -71.96579°)", " To: Irbid at (32.55556°, 35.85°)", "Step 2: Calculate longitude difference", " Δlon = 35.85 - -71.96579 = 107.8158°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 55.13°", "Step 5: Determine cardinal direction", " 55.1° → NE", "FINAL ANSWER: 55.13° (NE)" ] }, { "task": "bearing_computation", "point_a": { "lat": 7.75624, "lon": -8.8179, "name": "Nzérékoré" }, "point_b": { "lat": 45.82058, "lon": 8.82511, "name": "Varese" }, "ground_truth": { "initial_bearing_deg": 18.79, "cardinal_direction": "N", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Nzérékoré at (7.75624°, -8.8179°)", " To: Varese at (45.82058°, 8.82511°)", "Step 2: Calculate longitude difference", " Δlon = 8.82511 - -8.8179 = 17.6430°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 18.79°", "Step 5: Determine cardinal direction", " 18.8° → N", "FINAL ANSWER: 18.79° (N)" ] }, { "task": "bearing_computation", "point_a": { "lat": 55.78363, "lon": 37.47137, "name": "Khoroshëvo-Mnevniki" }, "point_b": { "lat": 2.34464, "lon": 42.27644, "name": "Baardheere" }, "ground_truth": { "initial_bearing_deg": 174.03, "cardinal_direction": "S", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Khoroshëvo-Mnevniki at (55.78363°, 37.47137°)", " To: Baardheere at (2.34464°, 42.27644°)", "Step 2: Calculate longitude difference", " Δlon = 42.27644 - 37.47137 = 4.8051°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 174.03°", "Step 5: Determine cardinal direction", " 174.0° → S", "FINAL ANSWER: 174.03° (S)" ] }, { "task": "bearing_computation", "point_a": { "lat": 10.0477, "lon": 78.74719, "name": "Sankarapatti" }, "point_b": { "lat": -12.3644, "lon": 13.53601, "name": "Lobito" }, "ground_truth": { "initial_bearing_deg": 252.34, "cardinal_direction": "W", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Sankarapatti at (10.0477°, 78.74719°)", " To: Lobito at (-12.3644°, 13.53601°)", "Step 2: Calculate longitude difference", " Δlon = 13.53601 - 78.74719 = -65.2112°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 252.34°", "Step 5: Determine cardinal direction", " 252.3° → W", "FINAL ANSWER: 252.34° (W)" ] }, { "task": "bearing_computation", "point_a": { "lat": 5.02208, "lon": -74.00481, "name": "Zipaquirá" }, "point_b": { "lat": 25.78924, "lon": 100.12279, "name": "Wanqiao Zhen" }, "ground_truth": { "initial_bearing_deg": 10.2, "cardinal_direction": "N", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Zipaquirá at (5.02208°, -74.00481°)", " To: Wanqiao Zhen at (25.78924°, 100.12279°)", "Step 2: Calculate longitude difference", " Δlon = 100.12279 - -74.00481 = 174.1276°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 10.20°", "Step 5: Determine cardinal direction", " 10.2° → N", "FINAL ANSWER: 10.20° (N)" ] }, { "task": "bearing_computation", "point_a": { "lat": 9.02871, "lon": 13.1848, "name": "Tchéboa" }, "point_b": { "lat": 54.12226, "lon": 17.98119, "name": "Kościerzyna" }, "ground_truth": { "initial_bearing_deg": 3.96, "cardinal_direction": "N", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Tchéboa at (9.02871°, 13.1848°)", " To: Kościerzyna at (54.12226°, 17.98119°)", "Step 2: Calculate longitude difference", " Δlon = 17.98119 - 13.1848 = 4.7964°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 3.96°", "Step 5: Determine cardinal direction", " 4.0° → N", "FINAL ANSWER: 3.96° (N)" ] }, { "task": "bearing_computation", "point_a": { "lat": 13.18421, "lon": 30.21669, "name": "El Obeid" }, "point_b": { "lat": 52.30322, "lon": 13.25405, "name": "Ludwigsfelde" }, "ground_truth": { "initial_bearing_deg": 344.35, "cardinal_direction": "N", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: El Obeid at (13.18421°, 30.21669°)", " To: Ludwigsfelde at (52.30322°, 13.25405°)", "Step 2: Calculate longitude difference", " Δlon = 13.25405 - 30.21669 = -16.9626°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 344.35°", "Step 5: Determine cardinal direction", " 344.4° → N", "FINAL ANSWER: 344.35° (N)" ] }, { "task": "bearing_computation", "point_a": { "lat": 19.22031, "lon": -70.53101, "name": "La Vega" }, "point_b": { "lat": 35.555, "lon": 5.61056, "name": "N’Gaous" }, "ground_truth": { "initial_bearing_deg": 58.45, "cardinal_direction": "NE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: La Vega at (19.22031°, -70.53101°)", " To: N’Gaous at (35.555°, 5.61056°)", "Step 2: Calculate longitude difference", " Δlon = 5.61056 - -70.53101 = 76.1416°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 58.45°", "Step 5: Determine cardinal direction", " 58.5° → NE", "FINAL ANSWER: 58.45° (NE)" ] }, { "task": "bearing_computation", "point_a": { "lat": 9.59972, "lon": 43.335, "name": "Tog Wajaale" }, "point_b": { "lat": 40.30428, "lon": -74.10042, "name": "Tinton Falls" }, "ground_truth": { "initial_bearing_deg": 315.82, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Tog Wajaale at (9.59972°, 43.335°)", " To: Tinton Falls at (40.30428°, -74.10042°)", "Step 2: Calculate longitude difference", " Δlon = -74.10042 - 43.335 = -117.4354°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 315.82°", "Step 5: Determine cardinal direction", " 315.8° → NW", "FINAL ANSWER: 315.82° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 26.51393, "lon": 85.29341, "name": "Sheohar" }, "point_b": { "lat": 33.85844, "lon": -84.3402, "name": "Brookhaven" }, "ground_truth": { "initial_bearing_deg": 350.18, "cardinal_direction": "N", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Sheohar at (26.51393°, 85.29341°)", " To: Brookhaven at (33.85844°, -84.3402°)", "Step 2: Calculate longitude difference", " Δlon = -84.3402 - 85.29341 = -169.6336°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 350.18°", "Step 5: Determine cardinal direction", " 350.2° → N", "FINAL ANSWER: 350.18° (N)" ] }, { "task": "bearing_computation", "point_a": { "lat": -13.77333, "lon": -42.71417, "name": "Igaporã" }, "point_b": { "lat": 13.42722, "lon": -16.68528, "name": "Bununka Kunda" }, "ground_truth": { "initial_bearing_deg": 44.55, "cardinal_direction": "NE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Igaporã at (-13.77333°, -42.71417°)", " To: Bununka Kunda at (13.42722°, -16.68528°)", "Step 2: Calculate longitude difference", " Δlon = -16.68528 - -42.71417 = 26.0289°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 44.55°", "Step 5: Determine cardinal direction", " 44.5° → NE", "FINAL ANSWER: 44.55° (NE)" ] }, { "task": "bearing_computation", "point_a": { "lat": 30.71877, "lon": 31.56299, "name": "Al Ibrāhīmīyah" }, "point_b": { "lat": -2.51389, "lon": -66.09167, "name": "Fonte Boa" }, "ground_truth": { "initial_bearing_deg": 271.75, "cardinal_direction": "W", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Al Ibrāhīmīyah at (30.71877°, 31.56299°)", " To: Fonte Boa at (-2.51389°, -66.09167°)", "Step 2: Calculate longitude difference", " Δlon = -66.09167 - 31.56299 = -97.6547°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 271.75°", "Step 5: Determine cardinal direction", " 271.8° → W", "FINAL ANSWER: 271.75° (W)" ] }, { "task": "bearing_computation", "point_a": { "lat": 60.40338, "lon": 25.105, "name": "Kerava" }, "point_b": { "lat": 29.35896, "lon": 30.68061, "name": "Ibshawāy" }, "ground_truth": { "initial_bearing_deg": 170.61, "cardinal_direction": "S", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Kerava at (60.40338°, 25.105°)", " To: Ibshawāy at (29.35896°, 30.68061°)", "Step 2: Calculate longitude difference", " Δlon = 30.68061 - 25.105 = 5.5756°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 170.61°", "Step 5: Determine cardinal direction", " 170.6° → S", "FINAL ANSWER: 170.61° (S)" ] }, { "task": "bearing_computation", "point_a": { "lat": 41.38555, "lon": 60.36408, "name": "Xiva" }, "point_b": { "lat": -19.19694, "lon": -40.09778, "name": "Sooretama" }, "ground_truth": { "initial_bearing_deg": 261.83, "cardinal_direction": "W", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Xiva at (41.38555°, 60.36408°)", " To: Sooretama at (-19.19694°, -40.09778°)", "Step 2: Calculate longitude difference", " Δlon = -40.09778 - 60.36408 = -100.4619°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 261.83°", "Step 5: Determine cardinal direction", " 261.8° → W", "FINAL ANSWER: 261.83° (W)" ] }, { "task": "bearing_computation", "point_a": { "lat": 29.373, "lon": 78.13636, "name": "Bijnor" }, "point_b": { "lat": 59.91273, "lon": 10.74609, "name": "Oslo" }, "ground_truth": { "initial_bearing_deg": 324.94, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Bijnor at (29.373°, 78.13636°)", " To: Oslo at (59.91273°, 10.74609°)", "Step 2: Calculate longitude difference", " Δlon = 10.74609 - 78.13636 = -67.3903°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 324.94°", "Step 5: Determine cardinal direction", " 324.9° → NW", "FINAL ANSWER: 324.94° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 12.75975, "lon": 75.20169, "name": "Puttūr" }, "point_b": { "lat": 11.8235, "lon": -70.25637, "name": "Santa Cruz de los Taques" }, "ground_truth": { "initial_bearing_deg": 304.25, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Puttūr at (12.75975°, 75.20169°)", " To: Santa Cruz de los Taques at (11.8235°, -70.25637°)", "Step 2: Calculate longitude difference", " Δlon = -70.25637 - 75.20169 = -145.4581°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 304.25°", "Step 5: Determine cardinal direction", " 304.2° → NW", "FINAL ANSWER: 304.25° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 19.68006, "lon": -103.2514, "name": "Tamazula de Gordiano" }, "point_b": { "lat": 12.37136, "lon": -1.41468, "name": "Saaba" }, "ground_truth": { "initial_bearing_deg": 74.27, "cardinal_direction": "E", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Tamazula de Gordiano at (19.68006°, -103.2514°)", " To: Saaba at (12.37136°, -1.41468°)", "Step 2: Calculate longitude difference", " Δlon = -1.41468 - -103.2514 = 101.8367°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 74.27°", "Step 5: Determine cardinal direction", " 74.3° → E", "FINAL ANSWER: 74.27° (E)" ] }, { "task": "bearing_computation", "point_a": { "lat": 5.26598, "lon": -76.56487, "name": "Tadó" }, "point_b": { "lat": 28.31457, "lon": 74.28952, "name": "Bhādāsar" }, "ground_truth": { "initial_bearing_deg": 38.3, "cardinal_direction": "NE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Tadó at (5.26598°, -76.56487°)", " To: Bhādāsar at (28.31457°, 74.28952°)", "Step 2: Calculate longitude difference", " Δlon = 74.28952 - -76.56487 = 150.8544°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 38.30°", "Step 5: Determine cardinal direction", " 38.3° → NE", "FINAL ANSWER: 38.30° (NE)" ] }, { "task": "bearing_computation", "point_a": { "lat": -6.98111, "lon": -34.83389, "name": "Cabedelo" }, "point_b": { "lat": 35.72917, "lon": 10.58082, "name": "Msaken" }, "ground_truth": { "initial_bearing_deg": 41.7, "cardinal_direction": "NE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Cabedelo at (-6.98111°, -34.83389°)", " To: Msaken at (35.72917°, 10.58082°)", "Step 2: Calculate longitude difference", " Δlon = 10.58082 - -34.83389 = 45.4147°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 41.70°", "Step 5: Determine cardinal direction", " 41.7° → NE", "FINAL ANSWER: 41.70° (NE)" ] }, { "task": "bearing_computation", "point_a": { "lat": 44.5432, "lon": 10.7848, "name": "Sassuolo" }, "point_b": { "lat": 58.7002, "lon": 59.4839, "name": "Kachkanar" }, "ground_truth": { "initial_bearing_deg": 46.65, "cardinal_direction": "NE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Sassuolo at (44.5432°, 10.7848°)", " To: Kachkanar at (58.7002°, 59.4839°)", "Step 2: Calculate longitude difference", " Δlon = 59.4839 - 10.7848 = 48.6991°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 46.65°", "Step 5: Determine cardinal direction", " 46.6° → NE", "FINAL ANSWER: 46.65° (NE)" ] }, { "task": "bearing_computation", "point_a": { "lat": 40.85843, "lon": -74.16376, "name": "Clifton" }, "point_b": { "lat": -3.55, "lon": 36.1, "name": "Makuyuni" }, "ground_truth": { "initial_bearing_deg": 79.16, "cardinal_direction": "E", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Clifton at (40.85843°, -74.16376°)", " To: Makuyuni at (-3.55°, 36.1°)", "Step 2: Calculate longitude difference", " Δlon = 36.1 - -74.16376 = 110.2638°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 79.16°", "Step 5: Determine cardinal direction", " 79.2° → E", "FINAL ANSWER: 79.16° (E)" ] }, { "task": "bearing_computation", "point_a": { "lat": 32.68833, "lon": 112.8275, "name": "Binhe" }, "point_b": { "lat": 60.81462, "lon": 23.62146, "name": "Forssa" }, "ground_truth": { "initial_bearing_deg": 326.3, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Binhe at (32.68833°, 112.8275°)", " To: Forssa at (60.81462°, 23.62146°)", "Step 2: Calculate longitude difference", " Δlon = 23.62146 - 112.8275 = -89.2060°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 326.30°", "Step 5: Determine cardinal direction", " 326.3° → NW", "FINAL ANSWER: 326.30° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": -34.71716, "lon": -55.9584, "name": "Pando" }, "point_b": { "lat": 32.28034, "lon": 119.16999, "name": "Zhenzhou" }, "ground_truth": { "initial_bearing_deg": 119.59, "cardinal_direction": "SE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Pando at (-34.71716°, -55.9584°)", " To: Zhenzhou at (32.28034°, 119.16999°)", "Step 2: Calculate longitude difference", " Δlon = 119.16999 - -55.9584 = 175.1284°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 119.59°", "Step 5: Determine cardinal direction", " 119.6° → SE", "FINAL ANSWER: 119.59° (SE)" ] }, { "task": "bearing_computation", "point_a": { "lat": 11.77554, "lon": 79.67016, "name": "Nellikkuppam" }, "point_b": { "lat": 35.42146, "lon": 133.24224, "name": "Yasugichō" }, "ground_truth": { "initial_bearing_deg": 54.45, "cardinal_direction": "NE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Nellikkuppam at (11.77554°, 79.67016°)", " To: Yasugichō at (35.42146°, 133.24224°)", "Step 2: Calculate longitude difference", " Δlon = 133.24224 - 79.67016 = 53.5721°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 54.45°", "Step 5: Determine cardinal direction", " 54.5° → NE", "FINAL ANSWER: 54.45° (NE)" ] }, { "task": "bearing_computation", "point_a": { "lat": -1.46771, "lon": 34.52279, "name": "Matongo" }, "point_b": { "lat": 31.18065, "lon": 31.86497, "name": "Al Jammālīyah" }, "ground_truth": { "initial_bearing_deg": 355.79, "cardinal_direction": "N", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Matongo at (-1.46771°, 34.52279°)", " To: Al Jammālīyah at (31.18065°, 31.86497°)", "Step 2: Calculate longitude difference", " Δlon = 31.86497 - 34.52279 = -2.6578°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 355.79°", "Step 5: Determine cardinal direction", " 355.8° → N", "FINAL ANSWER: 355.79° (N)" ] }, { "task": "bearing_computation", "point_a": { "lat": -16.575, "lon": -39.55333, "name": "Itabela" }, "point_b": { "lat": 6.27534, "lon": -6.99704, "name": "Buyo" }, "ground_truth": { "initial_bearing_deg": 57.27, "cardinal_direction": "NE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Itabela at (-16.575°, -39.55333°)", " To: Buyo at (6.27534°, -6.99704°)", "Step 2: Calculate longitude difference", " Δlon = -6.99704 - -39.55333 = 32.5563°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 57.27°", "Step 5: Determine cardinal direction", " 57.3° → NE", "FINAL ANSWER: 57.27° (NE)" ] }, { "task": "bearing_computation", "point_a": { "lat": 25.67927, "lon": -80.31727, "name": "Kendall" }, "point_b": { "lat": -28.21901, "lon": 152.03438, "name": "Warwick" }, "ground_truth": { "initial_bearing_deg": 254.54, "cardinal_direction": "W", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Kendall at (25.67927°, -80.31727°)", " To: Warwick at (-28.21901°, 152.03438°)", "Step 2: Calculate longitude difference", " Δlon = 152.03438 - -80.31727 = 232.3517°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 254.54°", "Step 5: Determine cardinal direction", " 254.5° → W", "FINAL ANSWER: 254.54° (W)" ] }, { "task": "bearing_computation", "point_a": { "lat": 42.9551, "lon": -81.62232, "name": "Strathroy" }, "point_b": { "lat": 40.64175, "lon": 15.80794, "name": "Potenza" }, "ground_truth": { "initial_bearing_deg": 54.16, "cardinal_direction": "NE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Strathroy at (42.9551°, -81.62232°)", " To: Potenza at (40.64175°, 15.80794°)", "Step 2: Calculate longitude difference", " Δlon = 15.80794 - -81.62232 = 97.4303°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 54.16°", "Step 5: Determine cardinal direction", " 54.2° → NE", "FINAL ANSWER: 54.16° (NE)" ] }, { "task": "bearing_computation", "point_a": { "lat": 25.10479, "lon": 84.1162, "name": "Nokha" }, "point_b": { "lat": -28.07071, "lon": 153.39329, "name": "Robina" }, "ground_truth": { "initial_bearing_deg": 124.09, "cardinal_direction": "SE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Nokha at (25.10479°, 84.1162°)", " To: Robina at (-28.07071°, 153.39329°)", "Step 2: Calculate longitude difference", " Δlon = 153.39329 - 84.1162 = 69.2771°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 124.09°", "Step 5: Determine cardinal direction", " 124.1° → SE", "FINAL ANSWER: 124.09° (SE)" ] }, { "task": "bearing_computation", "point_a": { "lat": 18.20107, "lon": -67.13962, "name": "Mayagüez" }, "point_b": { "lat": 53.59398, "lon": 142.95279, "name": "Okha" }, "ground_truth": { "initial_bearing_deg": 342.17, "cardinal_direction": "N", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Mayagüez at (18.20107°, -67.13962°)", " To: Okha at (53.59398°, 142.95279°)", "Step 2: Calculate longitude difference", " Δlon = 142.95279 - -67.13962 = 210.0924°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 342.17°", "Step 5: Determine cardinal direction", " 342.2° → N", "FINAL ANSWER: 342.17° (N)" ] }, { "task": "bearing_computation", "point_a": { "lat": 6.42611, "lon": 1.21333, "name": "Tsévié" }, "point_b": { "lat": 36.9, "lon": 7.76667, "name": "Annaba" }, "ground_truth": { "initial_bearing_deg": 10.19, "cardinal_direction": "N", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Tsévié at (6.42611°, 1.21333°)", " To: Annaba at (36.9°, 7.76667°)", "Step 2: Calculate longitude difference", " Δlon = 7.76667 - 1.21333 = 6.5533°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 10.19°", "Step 5: Determine cardinal direction", " 10.2° → N", "FINAL ANSWER: 10.19° (N)" ] }, { "task": "bearing_computation", "point_a": { "lat": 37.75018, "lon": -122.43369, "name": "Noe Valley" }, "point_b": { "lat": 27.9378, "lon": -82.28592, "name": "Brandon" }, "ground_truth": { "initial_bearing_deg": 94.32, "cardinal_direction": "E", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Noe Valley at (37.75018°, -122.43369°)", " To: Brandon at (27.9378°, -82.28592°)", "Step 2: Calculate longitude difference", " Δlon = -82.28592 - -122.43369 = 40.1478°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 94.32°", "Step 5: Determine cardinal direction", " 94.3° → E", "FINAL ANSWER: 94.32° (E)" ] }, { "task": "bearing_computation", "point_a": { "lat": 19.64186, "lon": 109.3545, "name": "Guangcun" }, "point_b": { "lat": 10.98133, "lon": 8.05749, "name": "Soba" }, "ground_truth": { "initial_bearing_deg": 284.23, "cardinal_direction": "W", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Guangcun at (19.64186°, 109.3545°)", " To: Soba at (10.98133°, 8.05749°)", "Step 2: Calculate longitude difference", " Δlon = 8.05749 - 109.3545 = -101.2970°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 284.23°", "Step 5: Determine cardinal direction", " 284.2° → W", "FINAL ANSWER: 284.23° (W)" ] }, { "task": "bearing_computation", "point_a": { "lat": 51.37281, "lon": -2.14002, "name": "Melksham" }, "point_b": { "lat": 47.42642, "lon": 9.65851, "name": "Lustenau" }, "ground_truth": { "initial_bearing_deg": 112.63, "cardinal_direction": "SE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Melksham at (51.37281°, -2.14002°)", " To: Lustenau at (47.42642°, 9.65851°)", "Step 2: Calculate longitude difference", " Δlon = 9.65851 - -2.14002 = 11.7985°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 112.63°", "Step 5: Determine cardinal direction", " 112.6° → SE", "FINAL ANSWER: 112.63° (SE)" ] }, { "task": "bearing_computation", "point_a": { "lat": 38.81144, "lon": -90.85291, "name": "Wentzville" }, "point_b": { "lat": -34.09345, "lon": 21.25725, "name": "Riversdale" }, "ground_truth": { "initial_bearing_deg": 107.47, "cardinal_direction": "E", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Wentzville at (38.81144°, -90.85291°)", " To: Riversdale at (-34.09345°, 21.25725°)", "Step 2: Calculate longitude difference", " Δlon = 21.25725 - -90.85291 = 112.1102°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 107.47°", "Step 5: Determine cardinal direction", " 107.5° → E", "FINAL ANSWER: 107.47° (E)" ] }, { "task": "bearing_computation", "point_a": { "lat": 31.34038, "lon": -110.93425, "name": "Nogales" }, "point_b": { "lat": 49.98037, "lon": 18.95382, "name": "Pszczyna" }, "ground_truth": { "initial_bearing_deg": 29.6, "cardinal_direction": "NE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Nogales at (31.34038°, -110.93425°)", " To: Pszczyna at (49.98037°, 18.95382°)", "Step 2: Calculate longitude difference", " Δlon = 18.95382 - -110.93425 = 129.8881°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 29.60°", "Step 5: Determine cardinal direction", " 29.6° → NE", "FINAL ANSWER: 29.60° (NE)" ] }, { "task": "bearing_computation", "point_a": { "lat": 36.87617, "lon": 6.90921, "name": "Skikda" }, "point_b": { "lat": -29.82068, "lon": 30.88674, "name": "Pinetown" }, "ground_truth": { "initial_bearing_deg": 158.02, "cardinal_direction": "S", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Skikda at (36.87617°, 6.90921°)", " To: Pinetown at (-29.82068°, 30.88674°)", "Step 2: Calculate longitude difference", " Δlon = 30.88674 - 6.90921 = 23.9775°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 158.02°", "Step 5: Determine cardinal direction", " 158.0° → S", "FINAL ANSWER: 158.02° (S)" ] }, { "task": "bearing_computation", "point_a": { "lat": -0.33316, "lon": 37.64587, "name": "Chuka" }, "point_b": { "lat": -4.30028, "lon": -38.49778, "name": "Chorozinho" }, "ground_truth": { "initial_bearing_deg": 265.65, "cardinal_direction": "W", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Chuka at (-0.33316°, 37.64587°)", " To: Chorozinho at (-4.30028°, -38.49778°)", "Step 2: Calculate longitude difference", " Δlon = -38.49778 - 37.64587 = -76.1437°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 265.65°", "Step 5: Determine cardinal direction", " 265.6° → W", "FINAL ANSWER: 265.65° (W)" ] }, { "task": "bearing_computation", "point_a": { "lat": -32.25215, "lon": 24.53075, "name": "Graaff Reinet" }, "point_b": { "lat": 35.75647, "lon": -83.97046, "name": "Maryville" }, "ground_truth": { "initial_bearing_deg": 294.87, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Graaff Reinet at (-32.25215°, 24.53075°)", " To: Maryville at (35.75647°, -83.97046°)", "Step 2: Calculate longitude difference", " Δlon = -83.97046 - 24.53075 = -108.5012°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 294.87°", "Step 5: Determine cardinal direction", " 294.9° → NW", "FINAL ANSWER: 294.87° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": -29.51694, "lon": -50.77778, "name": "Três Coroas" }, "point_b": { "lat": 52.48419, "lon": 13.53185, "name": "Karlshorst" }, "ground_truth": { "initial_bearing_deg": 33.78, "cardinal_direction": "NE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Três Coroas at (-29.51694°, -50.77778°)", " To: Karlshorst at (52.48419°, 13.53185°)", "Step 2: Calculate longitude difference", " Δlon = 13.53185 - -50.77778 = 64.3096°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 33.78°", "Step 5: Determine cardinal direction", " 33.8° → NE", "FINAL ANSWER: 33.78° (NE)" ] }, { "task": "bearing_computation", "point_a": { "lat": -12.48602, "lon": 130.9833, "name": "Palmerston" }, "point_b": { "lat": -7.00667, "lon": 39.29849, "name": "Vikindu" }, "ground_truth": { "initial_bearing_deg": 262.8, "cardinal_direction": "W", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Palmerston at (-12.48602°, 130.9833°)", " To: Vikindu at (-7.00667°, 39.29849°)", "Step 2: Calculate longitude difference", " Δlon = 39.29849 - 130.9833 = -91.6848°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 262.80°", "Step 5: Determine cardinal direction", " 262.8° → W", "FINAL ANSWER: 262.80° (W)" ] }, { "task": "bearing_computation", "point_a": { "lat": 12.33042, "lon": 76.60213, "name": "Hinakallu" }, "point_b": { "lat": 34.41639, "lon": 117.36306, "name": "Qingshanquan" }, "ground_truth": { "initial_bearing_deg": 52.14, "cardinal_direction": "NE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Hinakallu at (12.33042°, 76.60213°)", " To: Qingshanquan at (34.41639°, 117.36306°)", "Step 2: Calculate longitude difference", " Δlon = 117.36306 - 76.60213 = 40.7609°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 52.14°", "Step 5: Determine cardinal direction", " 52.1° → NE", "FINAL ANSWER: 52.14° (NE)" ] }, { "task": "bearing_computation", "point_a": { "lat": 32.46367, "lon": 44.41963, "name": "Al Ḩillah" }, "point_b": { "lat": 48.96833, "lon": 89.9625, "name": "Ölgii" }, "ground_truth": { "initial_bearing_deg": 50.25, "cardinal_direction": "NE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Al Ḩillah at (32.46367°, 44.41963°)", " To: Ölgii at (48.96833°, 89.9625°)", "Step 2: Calculate longitude difference", " Δlon = 89.9625 - 44.41963 = 45.5429°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 50.25°", "Step 5: Determine cardinal direction", " 50.2° → NE", "FINAL ANSWER: 50.25° (NE)" ] }, { "task": "bearing_computation", "point_a": { "lat": 14.8888, "lon": 5.2692, "name": "Tahoua" }, "point_b": { "lat": 25.7076, "lon": -80.32561, "name": "Glenvar Heights" }, "ground_truth": { "initial_bearing_deg": 294.08, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Tahoua at (14.8888°, 5.2692°)", " To: Glenvar Heights at (25.7076°, -80.32561°)", "Step 2: Calculate longitude difference", " Δlon = -80.32561 - 5.2692 = -85.5948°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 294.08°", "Step 5: Determine cardinal direction", " 294.1° → NW", "FINAL ANSWER: 294.08° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 41.92208, "lon": 21.53483, "name": "Studeničani" }, "point_b": { "lat": 7.43383, "lon": 3.28788, "name": "Igbo-Ora" }, "ground_truth": { "initial_bearing_deg": 210.23, "cardinal_direction": "SW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Studeničani at (41.92208°, 21.53483°)", " To: Igbo-Ora at (7.43383°, 3.28788°)", "Step 2: Calculate longitude difference", " Δlon = 3.28788 - 21.53483 = -18.2469°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 210.23°", "Step 5: Determine cardinal direction", " 210.2° → SW", "FINAL ANSWER: 210.23° (SW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 47.48919, "lon": 19.07012, "name": "Budapest VIII. kerület" }, "point_b": { "lat": 20.21081, "lon": -101.13212, "name": "Yuriria" }, "ground_truth": { "initial_bearing_deg": 305.64, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Budapest VIII. kerület at (47.48919°, 19.07012°)", " To: Yuriria at (20.21081°, -101.13212°)", "Step 2: Calculate longitude difference", " Δlon = -101.13212 - 19.07012 = -120.2022°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 305.64°", "Step 5: Determine cardinal direction", " 305.6° → NW", "FINAL ANSWER: 305.64° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 7.3, "lon": 38.65, "name": "Kuyera" }, "point_b": { "lat": 1.99546, "lon": 112.93254, "name": "Kapit" }, "ground_truth": { "initial_bearing_deg": 89.99, "cardinal_direction": "E", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Kuyera at (7.3°, 38.65°)", " To: Kapit at (1.99546°, 112.93254°)", "Step 2: Calculate longitude difference", " Δlon = 112.93254 - 38.65 = 74.2825°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 89.99°", "Step 5: Determine cardinal direction", " 90.0° → E", "FINAL ANSWER: 89.99° (E)" ] }, { "task": "bearing_computation", "point_a": { "lat": 22.70256, "lon": 77.93494, "name": "Bābai" }, "point_b": { "lat": 52.3475, "lon": 5.98333, "name": "Epe" }, "ground_truth": { "initial_bearing_deg": 318.54, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Bābai at (22.70256°, 77.93494°)", " To: Epe at (52.3475°, 5.98333°)", "Step 2: Calculate longitude difference", " Δlon = 5.98333 - 77.93494 = -71.9516°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 318.54°", "Step 5: Determine cardinal direction", " 318.5° → NW", "FINAL ANSWER: 318.54° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 44.54394, "lon": -73.14791, "name": "Colchester" }, "point_b": { "lat": 0.29517, "lon": 32.50159, "name": "Kyengera" }, "ground_truth": { "initial_bearing_deg": 78.67, "cardinal_direction": "E", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Colchester at (44.54394°, -73.14791°)", " To: Kyengera at (0.29517°, 32.50159°)", "Step 2: Calculate longitude difference", " Δlon = 32.50159 - -73.14791 = 105.6495°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 78.67°", "Step 5: Determine cardinal direction", " 78.7° → E", "FINAL ANSWER: 78.67° (E)" ] }, { "task": "bearing_computation", "point_a": { "lat": 14.76011, "lon": 121.19993, "name": "Rodriguez" }, "point_b": { "lat": -37.78247, "lon": 145.31682, "name": "Mooroolbark" }, "ground_truth": { "initial_bearing_deg": 157.41, "cardinal_direction": "SE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Rodriguez at (14.76011°, 121.19993°)", " To: Mooroolbark at (-37.78247°, 145.31682°)", "Step 2: Calculate longitude difference", " Δlon = 145.31682 - 121.19993 = 24.1169°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 157.41°", "Step 5: Determine cardinal direction", " 157.4° → SE", "FINAL ANSWER: 157.41° (SE)" ] }, { "task": "bearing_computation", "point_a": { "lat": 11.0517, "lon": 124.0055, "name": "Bogo" }, "point_b": { "lat": 51.28087, "lon": 4.41813, "name": "Ekeren" }, "ground_truth": { "initial_bearing_deg": 326.6, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Bogo at (11.0517°, 124.0055°)", " To: Ekeren at (51.28087°, 4.41813°)", "Step 2: Calculate longitude difference", " Δlon = 4.41813 - 124.0055 = -119.5874°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 326.60°", "Step 5: Determine cardinal direction", " 326.6° → NW", "FINAL ANSWER: 326.60° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 35.9132, "lon": -79.05584, "name": "Chapel Hill" }, "point_b": { "lat": 38.96872, "lon": -77.3411, "name": "Reston" }, "ground_truth": { "initial_bearing_deg": 23.5, "cardinal_direction": "NE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Chapel Hill at (35.9132°, -79.05584°)", " To: Reston at (38.96872°, -77.3411°)", "Step 2: Calculate longitude difference", " Δlon = -77.3411 - -79.05584 = 1.7147°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 23.50°", "Step 5: Determine cardinal direction", " 23.5° → NE", "FINAL ANSWER: 23.50° (NE)" ] }, { "task": "bearing_computation", "point_a": { "lat": 31.61667, "lon": -2.21667, "name": "Béchar" }, "point_b": { "lat": -1.52823, "lon": -45.07862, "name": "Apicum-Açu" }, "ground_truth": { "initial_bearing_deg": 239.11, "cardinal_direction": "SW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Béchar at (31.61667°, -2.21667°)", " To: Apicum-Açu at (-1.52823°, -45.07862°)", "Step 2: Calculate longitude difference", " Δlon = -45.07862 - -2.21667 = -42.8620°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 239.11°", "Step 5: Determine cardinal direction", " 239.1° → SW", "FINAL ANSWER: 239.11° (SW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 31.50777, "lon": 35.02929, "name": "Dūrā" }, "point_b": { "lat": 45.84806, "lon": 62.15254, "name": "Novokazalinsk" }, "ground_truth": { "initial_bearing_deg": 47.82, "cardinal_direction": "NE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Dūrā at (31.50777°, 35.02929°)", " To: Novokazalinsk at (45.84806°, 62.15254°)", "Step 2: Calculate longitude difference", " Δlon = 62.15254 - 35.02929 = 27.1232°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 47.82°", "Step 5: Determine cardinal direction", " 47.8° → NE", "FINAL ANSWER: 47.82° (NE)" ] }, { "task": "bearing_computation", "point_a": { "lat": -20.03841, "lon": 57.65055, "name": "Goodlands" }, "point_b": { "lat": 26.71194, "lon": 107.81139, "name": "Dafengdong" }, "ground_truth": { "initial_bearing_deg": 47.96, "cardinal_direction": "NE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Goodlands at (-20.03841°, 57.65055°)", " To: Dafengdong at (26.71194°, 107.81139°)", "Step 2: Calculate longitude difference", " Δlon = 107.81139 - 57.65055 = 50.1608°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 47.96°", "Step 5: Determine cardinal direction", " 48.0° → NE", "FINAL ANSWER: 47.96° (NE)" ] }, { "task": "bearing_computation", "point_a": { "lat": -25.699, "lon": 27.47475, "name": "Marikana" }, "point_b": { "lat": -19.57328, "lon": 18.1003, "name": "Grootfontein" }, "ground_truth": { "initial_bearing_deg": 303.41, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Marikana at (-25.699°, 27.47475°)", " To: Grootfontein at (-19.57328°, 18.1003°)", "Step 2: Calculate longitude difference", " Δlon = 18.1003 - 27.47475 = -9.3744°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 303.41°", "Step 5: Determine cardinal direction", " 303.4° → NW", "FINAL ANSWER: 303.41° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 55.32058, "lon": 42.17402, "name": "Vyksa" }, "point_b": { "lat": 1.30306, "lon": 103.90778, "name": "Marine Parade" }, "ground_truth": { "initial_bearing_deg": 113.15, "cardinal_direction": "SE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Vyksa at (55.32058°, 42.17402°)", " To: Marine Parade at (1.30306°, 103.90778°)", "Step 2: Calculate longitude difference", " Δlon = 103.90778 - 42.17402 = 61.7338°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 113.15°", "Step 5: Determine cardinal direction", " 113.2° → SE", "FINAL ANSWER: 113.15° (SE)" ] }, { "task": "bearing_computation", "point_a": { "lat": 48.89452, "lon": 18.04436, "name": "Trenčín" }, "point_b": { "lat": 16.455, "lon": 120.5875, "name": "La Trinidad" }, "ground_truth": { "initial_bearing_deg": 69.87, "cardinal_direction": "E", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Trenčín at (48.89452°, 18.04436°)", " To: La Trinidad at (16.455°, 120.5875°)", "Step 2: Calculate longitude difference", " Δlon = 120.5875 - 18.04436 = 102.5431°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 69.87°", "Step 5: Determine cardinal direction", " 69.9° → E", "FINAL ANSWER: 69.87° (E)" ] }, { "task": "bearing_computation", "point_a": { "lat": 19.15633, "lon": 96.34593, "name": "Yedashe" }, "point_b": { "lat": 56.1, "lon": 38.13333, "name": "Krasnoarmeysk" }, "ground_truth": { "initial_bearing_deg": 325.42, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Yedashe at (19.15633°, 96.34593°)", " To: Krasnoarmeysk at (56.1°, 38.13333°)", "Step 2: Calculate longitude difference", " Δlon = 38.13333 - 96.34593 = -58.2126°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 325.42°", "Step 5: Determine cardinal direction", " 325.4° → NW", "FINAL ANSWER: 325.42° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 41.11919, "lon": 70.09406, "name": "Yangiobod" }, "point_b": { "lat": 15.42977, "lon": 75.62971, "name": "Gadag" }, "ground_truth": { "initial_bearing_deg": 167.81, "cardinal_direction": "S", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Yangiobod at (41.11919°, 70.09406°)", " To: Gadag at (15.42977°, 75.62971°)", "Step 2: Calculate longitude difference", " Δlon = 75.62971 - 70.09406 = 5.5357°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 167.81°", "Step 5: Determine cardinal direction", " 167.8° → S", "FINAL ANSWER: 167.81° (S)" ] }, { "task": "bearing_computation", "point_a": { "lat": -12.46113, "lon": 130.84185, "name": "Darwin" }, "point_b": { "lat": 13.69889, "lon": 100.51244, "name": "Bang Khlo" }, "ground_truth": { "initial_bearing_deg": 310.04, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Darwin at (-12.46113°, 130.84185°)", " To: Bang Khlo at (13.69889°, 100.51244°)", "Step 2: Calculate longitude difference", " Δlon = 100.51244 - 130.84185 = -30.3294°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 310.04°", "Step 5: Determine cardinal direction", " 310.0° → NW", "FINAL ANSWER: 310.04° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": -37.8329, "lon": 145.0367, "name": "Hawthorn South" }, "point_b": { "lat": 14.42196, "lon": -16.96375, "name": "Mbour" }, "ground_truth": { "initial_bearing_deg": 219.1, "cardinal_direction": "SW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Hawthorn South at (-37.8329°, 145.0367°)", " To: Mbour at (14.42196°, -16.96375°)", "Step 2: Calculate longitude difference", " Δlon = -16.96375 - 145.0367 = -162.0005°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 219.10°", "Step 5: Determine cardinal direction", " 219.1° → SW", "FINAL ANSWER: 219.10° (SW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 35.53227, "lon": -97.95505, "name": "El Reno" }, "point_b": { "lat": -37.76722, "lon": 144.76657, "name": "Deer Park" }, "ground_truth": { "initial_bearing_deg": 247.72, "cardinal_direction": "W", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: El Reno at (35.53227°, -97.95505°)", " To: Deer Park at (-37.76722°, 144.76657°)", "Step 2: Calculate longitude difference", " Δlon = 144.76657 - -97.95505 = 242.7216°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 247.72°", "Step 5: Determine cardinal direction", " 247.7° → W", "FINAL ANSWER: 247.72° (W)" ] }, { "task": "bearing_computation", "point_a": { "lat": 53.14362, "lon": 0.3363, "name": "Skegness" }, "point_b": { "lat": 8.13333, "lon": 81.43333, "name": "Vakarai" }, "ground_truth": { "initial_bearing_deg": 92.21, "cardinal_direction": "E", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Skegness at (53.14362°, 0.3363°)", " To: Vakarai at (8.13333°, 81.43333°)", "Step 2: Calculate longitude difference", " Δlon = 81.43333 - 0.3363 = 81.0970°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 92.21°", "Step 5: Determine cardinal direction", " 92.2° → E", "FINAL ANSWER: 92.21° (E)" ] }, { "task": "bearing_computation", "point_a": { "lat": 43.30491, "lon": 13.72068, "name": "Civitanova Marche" }, "point_b": { "lat": 8.75225, "lon": 38.97846, "name": "Bishoftu" }, "ground_truth": { "initial_bearing_deg": 139.99, "cardinal_direction": "SE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Civitanova Marche at (43.30491°, 13.72068°)", " To: Bishoftu at (8.75225°, 38.97846°)", "Step 2: Calculate longitude difference", " Δlon = 38.97846 - 13.72068 = 25.2578°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 139.99°", "Step 5: Determine cardinal direction", " 140.0° → SE", "FINAL ANSWER: 139.99° (SE)" ] }, { "task": "bearing_computation", "point_a": { "lat": -8.57472, "lon": -36.87417, "name": "Venturosa" }, "point_b": { "lat": 12.24661, "lon": -1.58402, "name": "Zinguédéssé" }, "ground_truth": { "initial_bearing_deg": 59.79, "cardinal_direction": "NE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Venturosa at (-8.57472°, -36.87417°)", " To: Zinguédéssé at (12.24661°, -1.58402°)", "Step 2: Calculate longitude difference", " Δlon = -1.58402 - -36.87417 = 35.2901°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 59.79°", "Step 5: Determine cardinal direction", " 59.8° → NE", "FINAL ANSWER: 59.79° (NE)" ] }, { "task": "bearing_computation", "point_a": { "lat": 34.50344, "lon": -82.65013, "name": "Anderson" }, "point_b": { "lat": 35.33638, "lon": 139.40434, "name": "Chigasaki" }, "ground_truth": { "initial_bearing_deg": 326.31, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Anderson at (34.50344°, -82.65013°)", " To: Chigasaki at (35.33638°, 139.40434°)", "Step 2: Calculate longitude difference", " Δlon = 139.40434 - -82.65013 = 222.0545°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 326.31°", "Step 5: Determine cardinal direction", " 326.3° → NW", "FINAL ANSWER: 326.31° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 9.95689, "lon": -84.03209, "name": "Purral" }, "point_b": { "lat": 35.84509, "lon": 127.14752, "name": "Wanju" }, "ground_truth": { "initial_bearing_deg": 328.94, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Purral at (9.95689°, -84.03209°)", " To: Wanju at (35.84509°, 127.14752°)", "Step 2: Calculate longitude difference", " Δlon = 127.14752 - -84.03209 = 211.1796°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 328.94°", "Step 5: Determine cardinal direction", " 328.9° → NW", "FINAL ANSWER: 328.94° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": -25.85583, "lon": -52.52333, "name": "Chopinzinho" }, "point_b": { "lat": 7.82719, "lon": 6.07502, "name": "Kabba" }, "ground_truth": { "initial_bearing_deg": 67.65, "cardinal_direction": "E", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Chopinzinho at (-25.85583°, -52.52333°)", " To: Kabba at (7.82719°, 6.07502°)", "Step 2: Calculate longitude difference", " Δlon = 6.07502 - -52.52333 = 58.5984°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 67.65°", "Step 5: Determine cardinal direction", " 67.7° → E", "FINAL ANSWER: 67.65° (E)" ] }, { "task": "bearing_computation", "point_a": { "lat": 8.91587, "lon": 17.55046, "name": "Koumra" }, "point_b": { "lat": -17.345, "lon": -44.94194, "name": "Pirapora" }, "ground_truth": { "initial_bearing_deg": 246.8, "cardinal_direction": "SW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Koumra at (8.91587°, 17.55046°)", " To: Pirapora at (-17.345°, -44.94194°)", "Step 2: Calculate longitude difference", " Δlon = -44.94194 - 17.55046 = -62.4924°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 246.80°", "Step 5: Determine cardinal direction", " 246.8° → SW", "FINAL ANSWER: 246.80° (SW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 36.81058, "lon": 10.13481, "name": "Le Bardo" }, "point_b": { "lat": -33.88834, "lon": 151.12274, "name": "Ashfield" }, "ground_truth": { "initial_bearing_deg": 96.54, "cardinal_direction": "E", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Le Bardo at (36.81058°, 10.13481°)", " To: Ashfield at (-33.88834°, 151.12274°)", "Step 2: Calculate longitude difference", " Δlon = 151.12274 - 10.13481 = 140.9879°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 96.54°", "Step 5: Determine cardinal direction", " 96.5° → E", "FINAL ANSWER: 96.54° (E)" ] }, { "task": "bearing_computation", "point_a": { "lat": 36.45833, "lon": 7.51389, "name": "Boumahra Ahmed" }, "point_b": { "lat": 25.53852, "lon": 87.57044, "name": "Katihar" }, "ground_truth": { "initial_bearing_deg": 74.04, "cardinal_direction": "E", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Boumahra Ahmed at (36.45833°, 7.51389°)", " To: Katihar at (25.53852°, 87.57044°)", "Step 2: Calculate longitude difference", " Δlon = 87.57044 - 7.51389 = 80.0566°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 74.04°", "Step 5: Determine cardinal direction", " 74.0° → E", "FINAL ANSWER: 74.04° (E)" ] }, { "task": "bearing_computation", "point_a": { "lat": 42.07593, "lon": 21.05179, "name": "Tearce" }, "point_b": { "lat": 36.76639, "lon": 3.47717, "name": "Boumerdas" }, "ground_truth": { "initial_bearing_deg": 254.41, "cardinal_direction": "W", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Tearce at (42.07593°, 21.05179°)", " To: Boumerdas at (36.76639°, 3.47717°)", "Step 2: Calculate longitude difference", " Δlon = 3.47717 - 21.05179 = -17.5746°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 254.41°", "Step 5: Determine cardinal direction", " 254.4° → W", "FINAL ANSWER: 254.41° (W)" ] }, { "task": "bearing_computation", "point_a": { "lat": -6.7559, "lon": 111.038, "name": "Pati" }, "point_b": { "lat": 55.86661, "lon": 48.35931, "name": "Volzhsk" }, "ground_truth": { "initial_bearing_deg": 329.68, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Pati at (-6.7559°, 111.038°)", " To: Volzhsk at (55.86661°, 48.35931°)", "Step 2: Calculate longitude difference", " Δlon = 48.35931 - 111.038 = -62.6787°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 329.68°", "Step 5: Determine cardinal direction", " 329.7° → NW", "FINAL ANSWER: 329.68° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 6.84684, "lon": -1.39612, "name": "Effiduase" }, "point_b": { "lat": 52.80842, "lon": 17.19961, "name": "Wągrowiec" }, "ground_truth": { "initial_bearing_deg": 14.94, "cardinal_direction": "N", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Effiduase at (6.84684°, -1.39612°)", " To: Wągrowiec at (52.80842°, 17.19961°)", "Step 2: Calculate longitude difference", " Δlon = 17.19961 - -1.39612 = 18.5957°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 14.94°", "Step 5: Determine cardinal direction", " 14.9° → N", "FINAL ANSWER: 14.94° (N)" ] }, { "task": "bearing_computation", "point_a": { "lat": -26.8089, "lon": -55.02147, "name": "Puerto Rico" }, "point_b": { "lat": -4.85889, "lon": -43.35611, "name": "Caxias" }, "ground_truth": { "initial_bearing_deg": 28.93, "cardinal_direction": "NE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Puerto Rico at (-26.8089°, -55.02147°)", " To: Caxias at (-4.85889°, -43.35611°)", "Step 2: Calculate longitude difference", " Δlon = -43.35611 - -55.02147 = 11.6654°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 28.93°", "Step 5: Determine cardinal direction", " 28.9° → NE", "FINAL ANSWER: 28.93° (NE)" ] }, { "task": "bearing_computation", "point_a": { "lat": 36.84774, "lon": 10.11083, "name": "Mnihla" }, "point_b": { "lat": 29.90565, "lon": 107.63853, "name": "Huwei" }, "ground_truth": { "initial_bearing_deg": 61.48, "cardinal_direction": "NE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Mnihla at (36.84774°, 10.11083°)", " To: Huwei at (29.90565°, 107.63853°)", "Step 2: Calculate longitude difference", " Δlon = 107.63853 - 10.11083 = 97.5277°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 61.48°", "Step 5: Determine cardinal direction", " 61.5° → NE", "FINAL ANSWER: 61.48° (NE)" ] }, { "task": "bearing_computation", "point_a": { "lat": -3.50306, "lon": -80.27306, "name": "Zarumilla" }, "point_b": { "lat": 39.98111, "lon": 125.24472, "name": "Kusŏng" }, "ground_truth": { "initial_bearing_deg": 331.15, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Zarumilla at (-3.50306°, -80.27306°)", " To: Kusŏng at (39.98111°, 125.24472°)", "Step 2: Calculate longitude difference", " Δlon = 125.24472 - -80.27306 = 205.5178°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 331.15°", "Step 5: Determine cardinal direction", " 331.1° → NW", "FINAL ANSWER: 331.15° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 41.13121, "lon": -74.36737, "name": "West Milford" }, "point_b": { "lat": 36.82657, "lon": 10.08974, "name": "Douar Hicher" }, "ground_truth": { "initial_bearing_deg": 63.31, "cardinal_direction": "NE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: West Milford at (41.13121°, -74.36737°)", " To: Douar Hicher at (36.82657°, 10.08974°)", "Step 2: Calculate longitude difference", " Δlon = 10.08974 - -74.36737 = 84.4571°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 63.31°", "Step 5: Determine cardinal direction", " 63.3° → NE", "FINAL ANSWER: 63.31° (NE)" ] }, { "task": "bearing_computation", "point_a": { "lat": 28.23937, "lon": 75.64035, "name": "Chidawa" }, "point_b": { "lat": 39.42417, "lon": 29.98333, "name": "Kütahya" }, "ground_truth": { "initial_bearing_deg": 298.82, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Chidawa at (28.23937°, 75.64035°)", " To: Kütahya at (39.42417°, 29.98333°)", "Step 2: Calculate longitude difference", " Δlon = 29.98333 - 75.64035 = -45.6570°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 298.82°", "Step 5: Determine cardinal direction", " 298.8° → NW", "FINAL ANSWER: 298.82° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": -18.06354, "lon": 44.02951, "name": "Maintirano" }, "point_b": { "lat": 35.79154, "lon": -78.78112, "name": "Cary" }, "ground_truth": { "initial_bearing_deg": 301.62, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Maintirano at (-18.06354°, 44.02951°)", " To: Cary at (35.79154°, -78.78112°)", "Step 2: Calculate longitude difference", " Δlon = -78.78112 - 44.02951 = -122.8106°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 301.62°", "Step 5: Determine cardinal direction", " 301.6° → NW", "FINAL ANSWER: 301.62° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": -38.0965, "lon": 145.26707, "name": "Cranbourne West" }, "point_b": { "lat": -23.56729, "lon": -46.69232, "name": "Pinheiros" }, "ground_truth": { "initial_bearing_deg": 167.66, "cardinal_direction": "S", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Cranbourne West at (-38.0965°, 145.26707°)", " To: Pinheiros at (-23.56729°, -46.69232°)", "Step 2: Calculate longitude difference", " Δlon = -46.69232 - 145.26707 = -191.9594°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 167.66°", "Step 5: Determine cardinal direction", " 167.7° → S", "FINAL ANSWER: 167.66° (S)" ] }, { "task": "bearing_computation", "point_a": { "lat": 38.93067, "lon": -77.04081, "name": "Mount Pleasant" }, "point_b": { "lat": 36.53628, "lon": 3.8334, "name": "Draa el Mizan" }, "ground_truth": { "initial_bearing_deg": 64.23, "cardinal_direction": "NE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Mount Pleasant at (38.93067°, -77.04081°)", " To: Draa el Mizan at (36.53628°, 3.8334°)", "Step 2: Calculate longitude difference", " Δlon = 3.8334 - -77.04081 = 80.8742°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 64.23°", "Step 5: Determine cardinal direction", " 64.2° → NE", "FINAL ANSWER: 64.23° (NE)" ] }, { "task": "bearing_computation", "point_a": { "lat": 42.34166, "lon": 130.41081, "name": "Unggi" }, "point_b": { "lat": 53.82901, "lon": -1.53834, "name": "Chapel Allerton" }, "ground_truth": { "initial_bearing_deg": 333.02, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Unggi at (42.34166°, 130.41081°)", " To: Chapel Allerton at (53.82901°, -1.53834°)", "Step 2: Calculate longitude difference", " Δlon = -1.53834 - 130.41081 = -131.9492°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 333.02°", "Step 5: Determine cardinal direction", " 333.0° → NW", "FINAL ANSWER: 333.02° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 27.6327, "lon": 85.52201, "name": "Banepā" }, "point_b": { "lat": 19.11683, "lon": -70.63595, "name": "Jarabacoa" }, "ground_truth": { "initial_bearing_deg": 331.07, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Banepā at (27.6327°, 85.52201°)", " To: Jarabacoa at (19.11683°, -70.63595°)", "Step 2: Calculate longitude difference", " Δlon = -70.63595 - 85.52201 = -156.1580°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 331.07°", "Step 5: Determine cardinal direction", " 331.1° → NW", "FINAL ANSWER: 331.07° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 36.74445, "lon": 49.40082, "name": "Manjīl" }, "point_b": { "lat": 10.3258, "lon": -72.31343, "name": "La Villa del Rosario" }, "ground_truth": { "initial_bearing_deg": 298.43, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Manjīl at (36.74445°, 49.40082°)", " To: La Villa del Rosario at (10.3258°, -72.31343°)", "Step 2: Calculate longitude difference", " Δlon = -72.31343 - 49.40082 = -121.7142°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 298.43°", "Step 5: Determine cardinal direction", " 298.4° → NW", "FINAL ANSWER: 298.43° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": -18.14307, "lon": 177.50691, "name": "Sigatoka" }, "point_b": { "lat": -36.96807, "lon": 174.79875, "name": "Mangere" }, "ground_truth": { "initial_bearing_deg": 186.67, "cardinal_direction": "S", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Sigatoka at (-18.14307°, 177.50691°)", " To: Mangere at (-36.96807°, 174.79875°)", "Step 2: Calculate longitude difference", " Δlon = 174.79875 - 177.50691 = -2.7082°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 186.67°", "Step 5: Determine cardinal direction", " 186.7° → S", "FINAL ANSWER: 186.67° (S)" ] }, { "task": "bearing_computation", "point_a": { "lat": 31.07287, "lon": 31.49503, "name": "Maḩallat Damanah" }, "point_b": { "lat": 60.26711, "lon": 24.84713, "name": "Myyrmäki" }, "ground_truth": { "initial_bearing_deg": 353.31, "cardinal_direction": "N", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Maḩallat Damanah at (31.07287°, 31.49503°)", " To: Myyrmäki at (60.26711°, 24.84713°)", "Step 2: Calculate longitude difference", " Δlon = 24.84713 - 31.49503 = -6.6479°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 353.31°", "Step 5: Determine cardinal direction", " 353.3° → N", "FINAL ANSWER: 353.31° (N)" ] }, { "task": "bearing_computation", "point_a": { "lat": 50.31297, "lon": 11.91261, "name": "Hof" }, "point_b": { "lat": 42.21421, "lon": -83.14992, "name": "Wyandotte" }, "ground_truth": { "initial_bearing_deg": 303.01, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Hof at (50.31297°, 11.91261°)", " To: Wyandotte at (42.21421°, -83.14992°)", "Step 2: Calculate longitude difference", " Δlon = -83.14992 - 11.91261 = -95.0625°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 303.01°", "Step 5: Determine cardinal direction", " 303.0° → NW", "FINAL ANSWER: 303.01° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 10.09085, "lon": -5.19482, "name": "Kaouara" }, "point_b": { "lat": 55.75, "lon": -4.03333, "name": "Meikle Earnock" }, "ground_truth": { "initial_bearing_deg": 0.91, "cardinal_direction": "N", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Kaouara at (10.09085°, -5.19482°)", " To: Meikle Earnock at (55.75°, -4.03333°)", "Step 2: Calculate longitude difference", " Δlon = -4.03333 - -5.19482 = 1.1615°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 0.91°", "Step 5: Determine cardinal direction", " 0.9° → N", "FINAL ANSWER: 0.91° (N)" ] }, { "task": "bearing_computation", "point_a": { "lat": 25.42595, "lon": -100.97963, "name": "Saltillo" }, "point_b": { "lat": 50.93333, "lon": 6.95, "name": "Köln" }, "ground_truth": { "initial_bearing_deg": 37.39, "cardinal_direction": "NE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Saltillo at (25.42595°, -100.97963°)", " To: Köln at (50.93333°, 6.95°)", "Step 2: Calculate longitude difference", " Δlon = 6.95 - -100.97963 = 107.9296°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 37.39°", "Step 5: Determine cardinal direction", " 37.4° → NE", "FINAL ANSWER: 37.39° (NE)" ] }, { "task": "bearing_computation", "point_a": { "lat": -17.13806, "lon": -49.98806, "name": "Indiara" }, "point_b": { "lat": 38.63706, "lon": -77.31109, "name": "Dale City" }, "ground_truth": { "initial_bearing_deg": 335.89, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Indiara at (-17.13806°, -49.98806°)", " To: Dale City at (38.63706°, -77.31109°)", "Step 2: Calculate longitude difference", " Δlon = -77.31109 - -49.98806 = -27.3230°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 335.89°", "Step 5: Determine cardinal direction", " 335.9° → NW", "FINAL ANSWER: 335.89° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 27.23818, "lon": 111.46214, "name": "Shaoyang" }, "point_b": { "lat": 37.66442, "lon": 139.03502, "name": "Kamo" }, "ground_truth": { "initial_bearing_deg": 58.78, "cardinal_direction": "NE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Shaoyang at (27.23818°, 111.46214°)", " To: Kamo at (37.66442°, 139.03502°)", "Step 2: Calculate longitude difference", " Δlon = 139.03502 - 111.46214 = 27.5729°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 58.78°", "Step 5: Determine cardinal direction", " 58.8° → NE", "FINAL ANSWER: 58.78° (NE)" ] }, { "task": "bearing_computation", "point_a": { "lat": -22.88583, "lon": -48.445, "name": "Botucatu" }, "point_b": { "lat": 21.11667, "lon": 105.86667, "name": "Cổ Lóa" }, "ground_truth": { "initial_bearing_deg": 89.29, "cardinal_direction": "E", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Botucatu at (-22.88583°, -48.445°)", " To: Cổ Lóa at (21.11667°, 105.86667°)", "Step 2: Calculate longitude difference", " Δlon = 105.86667 - -48.445 = 154.3117°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 89.29°", "Step 5: Determine cardinal direction", " 89.3° → E", "FINAL ANSWER: 89.29° (E)" ] }, { "task": "bearing_computation", "point_a": { "lat": -3.45571, "lon": -79.9637, "name": "Santa Rosa" }, "point_b": { "lat": 22.34835, "lon": 73.13313, "name": "Undera" }, "ground_truth": { "initial_bearing_deg": 51.76, "cardinal_direction": "NE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Santa Rosa at (-3.45571°, -79.9637°)", " To: Undera at (22.34835°, 73.13313°)", "Step 2: Calculate longitude difference", " Δlon = 73.13313 - -79.9637 = 153.0968°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 51.76°", "Step 5: Determine cardinal direction", " 51.8° → NE", "FINAL ANSWER: 51.76° (NE)" ] }, { "task": "bearing_computation", "point_a": { "lat": 40.9983, "lon": 71.67257, "name": "Namangan" }, "point_b": { "lat": 36.53628, "lon": 3.8334, "name": "Draa el Mizan" }, "ground_truth": { "initial_bearing_deg": 288.6, "cardinal_direction": "W", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Namangan at (40.9983°, 71.67257°)", " To: Draa el Mizan at (36.53628°, 3.8334°)", "Step 2: Calculate longitude difference", " Δlon = 3.8334 - 71.67257 = -67.8392°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 288.60°", "Step 5: Determine cardinal direction", " 288.6° → W", "FINAL ANSWER: 288.60° (W)" ] }, { "task": "bearing_computation", "point_a": { "lat": -33.92399, "lon": 151.22749, "name": "Kingsford" }, "point_b": { "lat": 37.3625, "lon": 38.52667, "name": "Bozova" }, "ground_truth": { "initial_bearing_deg": 294.38, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Kingsford at (-33.92399°, 151.22749°)", " To: Bozova at (37.3625°, 38.52667°)", "Step 2: Calculate longitude difference", " Δlon = 38.52667 - 151.22749 = -112.7008°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 294.38°", "Step 5: Determine cardinal direction", " 294.4° → NW", "FINAL ANSWER: 294.38° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 39.30927, "lon": -76.47496, "name": "Essex" }, "point_b": { "lat": -21.28861, "lon": -50.34, "name": "Birigui" }, "ground_truth": { "initial_bearing_deg": 153.15, "cardinal_direction": "SE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Essex at (39.30927°, -76.47496°)", " To: Birigui at (-21.28861°, -50.34°)", "Step 2: Calculate longitude difference", " Δlon = -50.34 - -76.47496 = 26.1350°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 153.15°", "Step 5: Determine cardinal direction", " 153.2° → SE", "FINAL ANSWER: 153.15° (SE)" ] }, { "task": "bearing_computation", "point_a": { "lat": -33.36889, "lon": 19.31095, "name": "Ceres" }, "point_b": { "lat": 51.95951, "lon": 4.54533, "name": "Ommoord" }, "ground_truth": { "initial_bearing_deg": 350.95, "cardinal_direction": "N", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Ceres at (-33.36889°, 19.31095°)", " To: Ommoord at (51.95951°, 4.54533°)", "Step 2: Calculate longitude difference", " Δlon = 4.54533 - 19.31095 = -14.7656°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 350.95°", "Step 5: Determine cardinal direction", " 350.9° → N", "FINAL ANSWER: 350.95° (N)" ] }, { "task": "bearing_computation", "point_a": { "lat": 4.775, "lon": 103.4162, "name": "Dungun" }, "point_b": { "lat": 51.22134, "lon": 4.46595, "name": "Deurne" }, "ground_truth": { "initial_bearing_deg": 321.76, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Dungun at (4.775°, 103.4162°)", " To: Deurne at (51.22134°, 4.46595°)", "Step 2: Calculate longitude difference", " Δlon = 4.46595 - 103.4162 = -98.9502°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 321.76°", "Step 5: Determine cardinal direction", " 321.8° → NW", "FINAL ANSWER: 321.76° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 13.74155, "lon": 76.9043, "name": "Sīra" }, "point_b": { "lat": -2.93323, "lon": 10.98178, "name": "Tchibanga" }, "ground_truth": { "initial_bearing_deg": 260.87, "cardinal_direction": "W", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Sīra at (13.74155°, 76.9043°)", " To: Tchibanga at (-2.93323°, 10.98178°)", "Step 2: Calculate longitude difference", " Δlon = 10.98178 - 76.9043 = -65.9225°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 260.87°", "Step 5: Determine cardinal direction", " 260.9° → W", "FINAL ANSWER: 260.87° (W)" ] }, { "task": "bearing_computation", "point_a": { "lat": 22.2475, "lon": -97.83665, "name": "Ciudad Madero" }, "point_b": { "lat": 34.92915, "lon": 43.48878, "name": "Bayjī" }, "ground_truth": { "initial_bearing_deg": 33.56, "cardinal_direction": "NE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Ciudad Madero at (22.2475°, -97.83665°)", " To: Bayjī at (34.92915°, 43.48878°)", "Step 2: Calculate longitude difference", " Δlon = 43.48878 - -97.83665 = 141.3254°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 33.56°", "Step 5: Determine cardinal direction", " 33.6° → NE", "FINAL ANSWER: 33.56° (NE)" ] }, { "task": "bearing_computation", "point_a": { "lat": 38.05, "lon": 23.83333, "name": "Melíssia" }, "point_b": { "lat": 13.83446, "lon": 44.11469, "name": "Dhī as Sufāl" }, "ground_truth": { "initial_bearing_deg": 137.94, "cardinal_direction": "SE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Melíssia at (38.05°, 23.83333°)", " To: Dhī as Sufāl at (13.83446°, 44.11469°)", "Step 2: Calculate longitude difference", " Δlon = 44.11469 - 23.83333 = 20.2814°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 137.94°", "Step 5: Determine cardinal direction", " 137.9° → SE", "FINAL ANSWER: 137.94° (SE)" ] }, { "task": "bearing_computation", "point_a": { "lat": 50.3505, "lon": 14.47411, "name": "Mělník" }, "point_b": { "lat": 25.27139, "lon": 55.30323, "name": "Nāyf" }, "ground_truth": { "initial_bearing_deg": 113.28, "cardinal_direction": "SE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Mělník at (50.3505°, 14.47411°)", " To: Nāyf at (25.27139°, 55.30323°)", "Step 2: Calculate longitude difference", " Δlon = 55.30323 - 14.47411 = 40.8291°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 113.28°", "Step 5: Determine cardinal direction", " 113.3° → SE", "FINAL ANSWER: 113.28° (SE)" ] }, { "task": "bearing_computation", "point_a": { "lat": 13.4, "lon": -14.21667, "name": "Farato" }, "point_b": { "lat": 25.13994, "lon": 85.84096, "name": "Sheikhpura" }, "ground_truth": { "initial_bearing_deg": 63.22, "cardinal_direction": "NE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Farato at (13.4°, -14.21667°)", " To: Sheikhpura at (25.13994°, 85.84096°)", "Step 2: Calculate longitude difference", " Δlon = 85.84096 - -14.21667 = 100.0576°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 63.22°", "Step 5: Determine cardinal direction", " 63.2° → NE", "FINAL ANSWER: 63.22° (NE)" ] }, { "task": "bearing_computation", "point_a": { "lat": 36.80377, "lon": 7.73684, "name": "El Hadjar" }, "point_b": { "lat": -37.66667, "lon": 145.01667, "name": "Lalor" }, "ground_truth": { "initial_bearing_deg": 104.7, "cardinal_direction": "E", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: El Hadjar at (36.80377°, 7.73684°)", " To: Lalor at (-37.66667°, 145.01667°)", "Step 2: Calculate longitude difference", " Δlon = 145.01667 - 7.73684 = 137.2798°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 104.70°", "Step 5: Determine cardinal direction", " 104.7° → E", "FINAL ANSWER: 104.70° (E)" ] }, { "task": "bearing_computation", "point_a": { "lat": 36.92917, "lon": 6.58556, "name": "Kerkera" }, "point_b": { "lat": 51.55295, "lon": 0.55962, "name": "South Benfleet" }, "ground_truth": { "initial_bearing_deg": 345.62, "cardinal_direction": "N", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Kerkera at (36.92917°, 6.58556°)", " To: South Benfleet at (51.55295°, 0.55962°)", "Step 2: Calculate longitude difference", " Δlon = 0.55962 - 6.58556 = -6.0259°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 345.62°", "Step 5: Determine cardinal direction", " 345.6° → N", "FINAL ANSWER: 345.62° (N)" ] }, { "task": "bearing_computation", "point_a": { "lat": 41.40916, "lon": -75.6649, "name": "Scranton" }, "point_b": { "lat": 25.48742, "lon": 28.97918, "name": "Mūţ" }, "ground_truth": { "initial_bearing_deg": 61.53, "cardinal_direction": "NE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Scranton at (41.40916°, -75.6649°)", " To: Mūţ at (25.48742°, 28.97918°)", "Step 2: Calculate longitude difference", " Δlon = 28.97918 - -75.6649 = 104.6441°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 61.53°", "Step 5: Determine cardinal direction", " 61.5° → NE", "FINAL ANSWER: 61.53° (NE)" ] }, { "task": "bearing_computation", "point_a": { "lat": 23.64824, "lon": -100.64334, "name": "Matehuala" }, "point_b": { "lat": 35.44934, "lon": 119.23607, "name": "Xihu" }, "ground_truth": { "initial_bearing_deg": 326.26, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Matehuala at (23.64824°, -100.64334°)", " To: Xihu at (35.44934°, 119.23607°)", "Step 2: Calculate longitude difference", " Δlon = 119.23607 - -100.64334 = 219.8794°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 326.26°", "Step 5: Determine cardinal direction", " 326.3° → NW", "FINAL ANSWER: 326.26° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 22.4382, "lon": 88.43205, "name": "Rajpur Sonarpur" }, "point_b": { "lat": 39.34788, "lon": -76.76997, "name": "Milford Mill" }, "ground_truth": { "initial_bearing_deg": 347.23, "cardinal_direction": "N", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Rajpur Sonarpur at (22.4382°, 88.43205°)", " To: Milford Mill at (39.34788°, -76.76997°)", "Step 2: Calculate longitude difference", " Δlon = -76.76997 - 88.43205 = -165.2020°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 347.23°", "Step 5: Determine cardinal direction", " 347.2° → N", "FINAL ANSWER: 347.23° (N)" ] }, { "task": "bearing_computation", "point_a": { "lat": 40.84816, "lon": -73.99764, "name": "Palisades Park" }, "point_b": { "lat": 10.78556, "lon": -0.85139, "name": "Bolgatanga" }, "ground_truth": { "initial_bearing_deg": 92.72, "cardinal_direction": "E", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Palisades Park at (40.84816°, -73.99764°)", " To: Bolgatanga at (10.78556°, -0.85139°)", "Step 2: Calculate longitude difference", " Δlon = -0.85139 - -73.99764 = 73.1463°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 92.72°", "Step 5: Determine cardinal direction", " 92.7° → E", "FINAL ANSWER: 92.72° (E)" ] }, { "task": "bearing_computation", "point_a": { "lat": -33.01529, "lon": 27.91162, "name": "East London" }, "point_b": { "lat": 38.32614, "lon": 26.30574, "name": "Çeşme" }, "ground_truth": { "initial_bearing_deg": 358.67, "cardinal_direction": "N", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: East London at (-33.01529°, 27.91162°)", " To: Çeşme at (38.32614°, 26.30574°)", "Step 2: Calculate longitude difference", " Δlon = 26.30574 - 27.91162 = -1.6059°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 358.67°", "Step 5: Determine cardinal direction", " 358.7° → N", "FINAL ANSWER: 358.67° (N)" ] }, { "task": "bearing_computation", "point_a": { "lat": 12.05267, "lon": 78.48023, "name": "Harūr" }, "point_b": { "lat": 45.58882, "lon": 9.19792, "name": "Nova Milanese" }, "ground_truth": { "initial_bearing_deg": 314.66, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Harūr at (12.05267°, 78.48023°)", " To: Nova Milanese at (45.58882°, 9.19792°)", "Step 2: Calculate longitude difference", " Δlon = 9.19792 - 78.48023 = -69.2823°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 314.66°", "Step 5: Determine cardinal direction", " 314.7° → NW", "FINAL ANSWER: 314.66° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 30.73916, "lon": 108.59976, "name": "Changtan" }, "point_b": { "lat": -33.2792, "lon": 115.71504, "name": "Australind" }, "ground_truth": { "initial_bearing_deg": 173.4, "cardinal_direction": "S", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Changtan at (30.73916°, 108.59976°)", " To: Australind at (-33.2792°, 115.71504°)", "Step 2: Calculate longitude difference", " Δlon = 115.71504 - 108.59976 = 7.1153°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 173.40°", "Step 5: Determine cardinal direction", " 173.4° → S", "FINAL ANSWER: 173.40° (S)" ] }, { "task": "bearing_computation", "point_a": { "lat": 33.39678, "lon": -84.59576, "name": "Peachtree City" }, "point_b": { "lat": 34.68406, "lon": 33.03794, "name": "Limassol" }, "ground_truth": { "initial_bearing_deg": 46.76, "cardinal_direction": "NE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Peachtree City at (33.39678°, -84.59576°)", " To: Limassol at (34.68406°, 33.03794°)", "Step 2: Calculate longitude difference", " Δlon = 33.03794 - -84.59576 = 117.6337°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 46.76°", "Step 5: Determine cardinal direction", " 46.8° → NE", "FINAL ANSWER: 46.76° (NE)" ] }, { "task": "bearing_computation", "point_a": { "lat": 40.72861, "lon": 124.78472, "name": "Kuandian" }, "point_b": { "lat": 39.42417, "lon": 29.98333, "name": "Kütahya" }, "ground_truth": { "initial_bearing_deg": 304.22, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Kuandian at (40.72861°, 124.78472°)", " To: Kütahya at (39.42417°, 29.98333°)", "Step 2: Calculate longitude difference", " Δlon = 29.98333 - 124.78472 = -94.8014°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 304.22°", "Step 5: Determine cardinal direction", " 304.2° → NW", "FINAL ANSWER: 304.22° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 12.63056, "lon": 39.03472, "name": "Sek’ot’a" }, "point_b": { "lat": 0.18333, "lon": 30.08333, "name": "Kasese" }, "ground_truth": { "initial_bearing_deg": 216.16, "cardinal_direction": "SW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Sek’ot’a at (12.63056°, 39.03472°)", " To: Kasese at (0.18333°, 30.08333°)", "Step 2: Calculate longitude difference", " Δlon = 30.08333 - 39.03472 = -8.9514°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 216.16°", "Step 5: Determine cardinal direction", " 216.2° → SW", "FINAL ANSWER: 216.16° (SW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 7.25597, "lon": -7.23508, "name": "Kouibly" }, "point_b": { "lat": 43.1689, "lon": -86.26395, "name": "Norton Shores" }, "ground_truth": { "initial_bearing_deg": 312.72, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Kouibly at (7.25597°, -7.23508°)", " To: Norton Shores at (43.1689°, -86.26395°)", "Step 2: Calculate longitude difference", " Δlon = -86.26395 - -7.23508 = -79.0289°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 312.72°", "Step 5: Determine cardinal direction", " 312.7° → NW", "FINAL ANSWER: 312.72° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 51.1681, "lon": 52.99782, "name": "Aqsay" }, "point_b": { "lat": 9.91861, "lon": -68.30472, "name": "Tinaquillo" }, "ground_truth": { "initial_bearing_deg": 301.05, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Aqsay at (51.1681°, 52.99782°)", " To: Tinaquillo at (9.91861°, -68.30472°)", "Step 2: Calculate longitude difference", " Δlon = -68.30472 - 52.99782 = -121.3025°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 301.05°", "Step 5: Determine cardinal direction", " 301.1° → NW", "FINAL ANSWER: 301.05° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 17.20667, "lon": -100.43306, "name": "Atoyac de Álvarez" }, "point_b": { "lat": 50.90769, "lon": 5.41875, "name": "Diepenbeek" }, "ground_truth": { "initial_bearing_deg": 37.44, "cardinal_direction": "NE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Atoyac de Álvarez at (17.20667°, -100.43306°)", " To: Diepenbeek at (50.90769°, 5.41875°)", "Step 2: Calculate longitude difference", " Δlon = 5.41875 - -100.43306 = 105.8518°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 37.44°", "Step 5: Determine cardinal direction", " 37.4° → NE", "FINAL ANSWER: 37.44° (NE)" ] }, { "task": "bearing_computation", "point_a": { "lat": -22.59861, "lon": -48.80028, "name": "Lençóis Paulista" }, "point_b": { "lat": -4.66667, "lon": 34.86667, "name": "Ilongero" }, "ground_truth": { "initial_bearing_deg": 91.9, "cardinal_direction": "E", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Lençóis Paulista at (-22.59861°, -48.80028°)", " To: Ilongero at (-4.66667°, 34.86667°)", "Step 2: Calculate longitude difference", " Δlon = 34.86667 - -48.80028 = 83.6669°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 91.90°", "Step 5: Determine cardinal direction", " 91.9° → E", "FINAL ANSWER: 91.90° (E)" ] }, { "task": "bearing_computation", "point_a": { "lat": 34.99921, "lon": 136.09674, "name": "Konan" }, "point_b": { "lat": -27.25204, "lon": 152.99226, "name": "Kallangur" }, "ground_truth": { "initial_bearing_deg": 163.33, "cardinal_direction": "S", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Konan at (34.99921°, 136.09674°)", " To: Kallangur at (-27.25204°, 152.99226°)", "Step 2: Calculate longitude difference", " Δlon = 152.99226 - 136.09674 = 16.8955°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 163.33°", "Step 5: Determine cardinal direction", " 163.3° → S", "FINAL ANSWER: 163.33° (S)" ] }, { "task": "bearing_computation", "point_a": { "lat": -12.6125, "lon": -38.29694, "name": "Dias d'Ávila" }, "point_b": { "lat": -25.77889, "lon": -49.32611, "name": "Mandirituba" }, "ground_truth": { "initial_bearing_deg": 216.67, "cardinal_direction": "SW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Dias d'Ávila at (-12.6125°, -38.29694°)", " To: Mandirituba at (-25.77889°, -49.32611°)", "Step 2: Calculate longitude difference", " Δlon = -49.32611 - -38.29694 = -11.0292°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 216.67°", "Step 5: Determine cardinal direction", " 216.7° → SW", "FINAL ANSWER: 216.67° (SW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 1.8681, "lon": 103.1124, "name": "Parit Raja" }, "point_b": { "lat": -9.11139, "lon": -37.12306, "name": "Águas Belas" }, "ground_truth": { "initial_bearing_deg": 258.06, "cardinal_direction": "W", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Parit Raja at (1.8681°, 103.1124°)", " To: Águas Belas at (-9.11139°, -37.12306°)", "Step 2: Calculate longitude difference", " Δlon = -37.12306 - 103.1124 = -140.2355°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 258.06°", "Step 5: Determine cardinal direction", " 258.1° → W", "FINAL ANSWER: 258.06° (W)" ] }, { "task": "bearing_computation", "point_a": { "lat": -34.75705, "lon": 138.60819, "name": "Paralowie" }, "point_b": { "lat": 48.0021, "lon": 0.20251, "name": "Le Mans" }, "ground_truth": { "initial_bearing_deg": 306.22, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Paralowie at (-34.75705°, 138.60819°)", " To: Le Mans at (48.0021°, 0.20251°)", "Step 2: Calculate longitude difference", " Δlon = 0.20251 - 138.60819 = -138.4057°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 306.22°", "Step 5: Determine cardinal direction", " 306.2° → NW", "FINAL ANSWER: 306.22° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 20.51167, "lon": -103.23689, "name": "San José del Castillo" }, "point_b": { "lat": -37.74124, "lon": 144.73631, "name": "Caroline Springs" }, "ground_truth": { "initial_bearing_deg": 237.37, "cardinal_direction": "SW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: San José del Castillo at (20.51167°, -103.23689°)", " To: Caroline Springs at (-37.74124°, 144.73631°)", "Step 2: Calculate longitude difference", " Δlon = 144.73631 - -103.23689 = 247.9732°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 237.37°", "Step 5: Determine cardinal direction", " 237.4° → SW", "FINAL ANSWER: 237.37° (SW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 42.49747, "lon": -94.16802, "name": "Fort Dodge" }, "point_b": { "lat": -24.51667, "lon": 28.71667, "name": "Mookgophong" }, "ground_truth": { "initial_bearing_deg": 87.92, "cardinal_direction": "E", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Fort Dodge at (42.49747°, -94.16802°)", " To: Mookgophong at (-24.51667°, 28.71667°)", "Step 2: Calculate longitude difference", " Δlon = 28.71667 - -94.16802 = 122.8847°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 87.92°", "Step 5: Determine cardinal direction", " 87.9° → E", "FINAL ANSWER: 87.92° (E)" ] }, { "task": "bearing_computation", "point_a": { "lat": 36.45833, "lon": 7.51389, "name": "Boumahra Ahmed" }, "point_b": { "lat": 34.1064, "lon": -117.37032, "name": "Rialto" }, "ground_truth": { "initial_bearing_deg": 317.16, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Boumahra Ahmed at (36.45833°, 7.51389°)", " To: Rialto at (34.1064°, -117.37032°)", "Step 2: Calculate longitude difference", " Δlon = -117.37032 - 7.51389 = -124.8842°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 317.16°", "Step 5: Determine cardinal direction", " 317.2° → NW", "FINAL ANSWER: 317.16° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 27.06309, "lon": 31.34425, "name": "As Sāḩil" }, "point_b": { "lat": -34.15152, "lon": 19.01509, "name": "Grabouw" }, "ground_truth": { "initial_bearing_deg": 191.51, "cardinal_direction": "S", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: As Sāḩil at (27.06309°, 31.34425°)", " To: Grabouw at (-34.15152°, 19.01509°)", "Step 2: Calculate longitude difference", " Δlon = 19.01509 - 31.34425 = -12.3292°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 191.51°", "Step 5: Determine cardinal direction", " 191.5° → S", "FINAL ANSWER: 191.51° (S)" ] }, { "task": "bearing_computation", "point_a": { "lat": 0.0607, "lon": 34.28806, "name": "Siaya" }, "point_b": { "lat": 53.32641, "lon": 9.86812, "name": "Buchholz in der Nordheide" }, "ground_truth": { "initial_bearing_deg": 342.88, "cardinal_direction": "N", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Siaya at (0.0607°, 34.28806°)", " To: Buchholz in der Nordheide at (53.32641°, 9.86812°)", "Step 2: Calculate longitude difference", " Δlon = 9.86812 - 34.28806 = -24.4199°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 342.88°", "Step 5: Determine cardinal direction", " 342.9° → N", "FINAL ANSWER: 342.88° (N)" ] }, { "task": "bearing_computation", "point_a": { "lat": 34.275, "lon": 133.75, "name": "Tadotsu" }, "point_b": { "lat": 44.1494, "lon": 43.47019, "name": "Georgiyevsk" }, "ground_truth": { "initial_bearing_deg": 308.83, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Tadotsu at (34.275°, 133.75°)", " To: Georgiyevsk at (44.1494°, 43.47019°)", "Step 2: Calculate longitude difference", " Δlon = 43.47019 - 133.75 = -90.2798°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 308.83°", "Step 5: Determine cardinal direction", " 308.8° → NW", "FINAL ANSWER: 308.83° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": -6.14755, "lon": 143.65633, "name": "Mendi" }, "point_b": { "lat": -19.39111, "lon": -40.07222, "name": "Linhares" }, "ground_truth": { "initial_bearing_deg": 171.9, "cardinal_direction": "S", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Mendi at (-6.14755°, 143.65633°)", " To: Linhares at (-19.39111°, -40.07222°)", "Step 2: Calculate longitude difference", " Δlon = -40.07222 - 143.65633 = -183.7285°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 171.90°", "Step 5: Determine cardinal direction", " 171.9° → S", "FINAL ANSWER: 171.90° (S)" ] }, { "task": "bearing_computation", "point_a": { "lat": 37.7966, "lon": -122.40858, "name": "Chinatown" }, "point_b": { "lat": -7.12056, "lon": -38.50194, "name": "São José de Piranhas" }, "ground_truth": { "initial_bearing_deg": 99.35, "cardinal_direction": "E", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Chinatown at (37.7966°, -122.40858°)", " To: São José de Piranhas at (-7.12056°, -38.50194°)", "Step 2: Calculate longitude difference", " Δlon = -38.50194 - -122.40858 = 83.9066°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 99.35°", "Step 5: Determine cardinal direction", " 99.3° → E", "FINAL ANSWER: 99.35° (E)" ] }, { "task": "bearing_computation", "point_a": { "lat": 5.89405, "lon": 5.67666, "name": "Sapele" }, "point_b": { "lat": 2.269, "lon": 102.1427, "name": "Sungai Udang" }, "ground_truth": { "initial_bearing_deg": 87.06, "cardinal_direction": "E", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Sapele at (5.89405°, 5.67666°)", " To: Sungai Udang at (2.269°, 102.1427°)", "Step 2: Calculate longitude difference", " Δlon = 102.1427 - 5.67666 = 96.4660°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 87.06°", "Step 5: Determine cardinal direction", " 87.1° → E", "FINAL ANSWER: 87.06° (E)" ] }, { "task": "bearing_computation", "point_a": { "lat": 42.81084, "lon": -1.66409, "name": "Ermitagaña" }, "point_b": { "lat": 28.25849, "lon": 42.92457, "name": "Turubah" }, "ground_truth": { "initial_bearing_deg": 97.28, "cardinal_direction": "E", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Ermitagaña at (42.81084°, -1.66409°)", " To: Turubah at (28.25849°, 42.92457°)", "Step 2: Calculate longitude difference", " Δlon = 42.92457 - -1.66409 = 44.5887°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 97.28°", "Step 5: Determine cardinal direction", " 97.3° → E", "FINAL ANSWER: 97.28° (E)" ] }, { "task": "bearing_computation", "point_a": { "lat": 34.34381, "lon": 3.22475, "name": "’Aïn el Bell" }, "point_b": { "lat": -34.61315, "lon": -58.37723, "name": "Buenos Aires" }, "ground_truth": { "initial_bearing_deg": 226.38, "cardinal_direction": "SW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: ’Aïn el Bell at (34.34381°, 3.22475°)", " To: Buenos Aires at (-34.61315°, -58.37723°)", "Step 2: Calculate longitude difference", " Δlon = -58.37723 - 3.22475 = -61.6020°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 226.38°", "Step 5: Determine cardinal direction", " 226.4° → SW", "FINAL ANSWER: 226.38° (SW)" ] }, { "task": "bearing_computation", "point_a": { "lat": -28.13442, "lon": -58.76685, "name": "San Lorenzo" }, "point_b": { "lat": 51.09242, "lon": 4.3717, "name": "Boom" }, "ground_truth": { "initial_bearing_deg": 34.34, "cardinal_direction": "NE", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: San Lorenzo at (-28.13442°, -58.76685°)", " To: Boom at (51.09242°, 4.3717°)", "Step 2: Calculate longitude difference", " Δlon = 4.3717 - -58.76685 = 63.1385°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 34.34°", "Step 5: Determine cardinal direction", " 34.3° → NE", "FINAL ANSWER: 34.34° (NE)" ] }, { "task": "bearing_computation", "point_a": { "lat": -18.11094, "lon": 178.40943, "name": "Lami" }, "point_b": { "lat": 36.20389, "lon": 127.08472, "name": "Nonsan" }, "ground_truth": { "initial_bearing_deg": 318.74, "cardinal_direction": "NW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Lami at (-18.11094°, 178.40943°)", " To: Nonsan at (36.20389°, 127.08472°)", "Step 2: Calculate longitude difference", " Δlon = 127.08472 - 178.40943 = -51.3247°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 318.74°", "Step 5: Determine cardinal direction", " 318.7° → NW", "FINAL ANSWER: 318.74° (NW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 33.86751, "lon": -117.99812, "name": "Buena Park" }, "point_b": { "lat": 59.51404, "lon": 15.99255, "name": "Köping" }, "ground_truth": { "initial_bearing_deg": 21.81, "cardinal_direction": "N", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Buena Park at (33.86751°, -117.99812°)", " To: Köping at (59.51404°, 15.99255°)", "Step 2: Calculate longitude difference", " Δlon = 15.99255 - -117.99812 = 133.9907°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 21.81°", "Step 5: Determine cardinal direction", " 21.8° → N", "FINAL ANSWER: 21.81° (N)" ] }, { "task": "bearing_computation", "point_a": { "lat": 43.73149, "lon": -79.42023, "name": "Bedford Park-Nortown" }, "point_b": { "lat": 34.36591, "lon": 107.35904, "name": "Guozhen" }, "ground_truth": { "initial_bearing_deg": 354.29, "cardinal_direction": "N", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Bedford Park-Nortown at (43.73149°, -79.42023°)", " To: Guozhen at (34.36591°, 107.35904°)", "Step 2: Calculate longitude difference", " Δlon = 107.35904 - -79.42023 = 186.7793°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 354.29°", "Step 5: Determine cardinal direction", " 354.3° → N", "FINAL ANSWER: 354.29° (N)" ] }, { "task": "bearing_computation", "point_a": { "lat": 44.95719, "lon": 34.11079, "name": "Simferopol" }, "point_b": { "lat": 29.86632, "lon": 77.89118, "name": "Roorkee" }, "ground_truth": { "initial_bearing_deg": 98.53, "cardinal_direction": "E", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Simferopol at (44.95719°, 34.11079°)", " To: Roorkee at (29.86632°, 77.89118°)", "Step 2: Calculate longitude difference", " Δlon = 77.89118 - 34.11079 = 43.7804°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 98.53°", "Step 5: Determine cardinal direction", " 98.5° → E", "FINAL ANSWER: 98.53° (E)" ] }, { "task": "bearing_computation", "point_a": { "lat": -22.97111, "lon": 30.67361, "name": "Malamulele" }, "point_b": { "lat": 53.14083, "lon": -6.06306, "name": "Greystones" }, "ground_truth": { "initial_bearing_deg": 338.78, "cardinal_direction": "N", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Malamulele at (-22.97111°, 30.67361°)", " To: Greystones at (53.14083°, -6.06306°)", "Step 2: Calculate longitude difference", " Δlon = -6.06306 - 30.67361 = -36.7367°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 338.78°", "Step 5: Determine cardinal direction", " 338.8° → N", "FINAL ANSWER: 338.78° (N)" ] }, { "task": "bearing_computation", "point_a": { "lat": -21.40611, "lon": -48.50472, "name": "Taquaritinga" }, "point_b": { "lat": -5.55694, "lon": -80.82222, "name": "Sechura" }, "ground_truth": { "initial_bearing_deg": 292.17, "cardinal_direction": "W", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Taquaritinga at (-21.40611°, -48.50472°)", " To: Sechura at (-5.55694°, -80.82222°)", "Step 2: Calculate longitude difference", " Δlon = -80.82222 - -48.50472 = -32.3175°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 292.17°", "Step 5: Determine cardinal direction", " 292.2° → W", "FINAL ANSWER: 292.17° (W)" ] }, { "task": "bearing_computation", "point_a": { "lat": 52.01682, "lon": 11.7307, "name": "Schönebeck" }, "point_b": { "lat": -22.39028, "lon": -44.96667, "name": "Passa Quatro" }, "ground_truth": { "initial_bearing_deg": 230.61, "cardinal_direction": "SW", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Schönebeck at (52.01682°, 11.7307°)", " To: Passa Quatro at (-22.39028°, -44.96667°)", "Step 2: Calculate longitude difference", " Δlon = -44.96667 - 11.7307 = -56.6974°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 230.61°", "Step 5: Determine cardinal direction", " 230.6° → SW", "FINAL ANSWER: 230.61° (SW)" ] }, { "task": "bearing_computation", "point_a": { "lat": 42.90395, "lon": -78.69225, "name": "Depew" }, "point_b": { "lat": 23.02389, "lon": -82.408, "name": "Fontanar" }, "ground_truth": { "initial_bearing_deg": 189.99, "cardinal_direction": "S", "tolerance_deg": 5.0 }, "reasoning_steps": [ "Step 1: Identify the coordinates", " From: Depew at (42.90395°, -78.69225°)", " To: Fontanar at (23.02389°, -82.408°)", "Step 2: Calculate longitude difference", " Δlon = -82.408 - -78.69225 = -3.7157°", "Step 3: Apply bearing formula", " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", "Step 4: Convert to degrees and normalize to 0-360°", " Initial bearing = 189.99°", "Step 5: Determine cardinal direction", " 190.0° → S", "FINAL ANSWER: 189.99° (S)" ] } ]