modularized

maths/geometry/cos_degrees.py

@@ -0,0 +1,5 @@
+import math
+
+def cos_degrees(angle):
+    """Calculate the cosine of an angle in degrees."""
+    return math.cos(math.radians(angle))

maths/geometry/inverse_trig_functions.py

@@ -0,0 +1,31 @@
+import math
+
+def inverse_trig_functions(value: float, function_name: str) -> str:
+    """
+    Calculates inverse trigonometric functions (asin, acos, atan) in degrees.
+    Args:
+        value: The value to calculate the inverse trigonometric function for.
+               For asin and acos, must be between -1 and 1.
+        function_name: "asin", "acos", or "atan".
+    Returns:
+        A string representing the result in degrees, or an error message.
+    """
+    if not isinstance(value, (int, float)):
+        return "Error: Input value must be a number."
+    func_name = function_name.lower()
+    result_rad = 0.0
+    if func_name == "asin":
+        if -1 <= value <= 1:
+            result_rad = math.asin(value)
+        else:
+            return "Error: Input for asin must be between -1 and 1."
+    elif func_name == "acos":
+        if -1 <= value <= 1:
+            result_rad = math.acos(value)
+        else:
+            return "Error: Input for acos must be between -1 and 1."
+    elif func_name == "atan":
+        result_rad = math.atan(value)
+    else:
+        return "Error: Invalid function name. Choose 'asin', 'acos', or 'atan'."
+    return f"{math.degrees(result_rad):.4f} degrees"

maths/geometry/sin_degrees.py

@@ -0,0 +1,5 @@
+import math
+
+def sin_degrees(angle):
+    """Calculate the sine of an angle in degrees."""
+    return math.sin(math.radians(angle))

maths/geometry/{trigonometry.py → solve_trig_equations.py}

@@ -1,80 +1,23 @@
-"""
-Trigonometry operations for high school level.
-"""
 import math
 
-def sin_degrees(angle):
-    """Calculate the sine of an angle in degrees."""
-    return math.sin(math.radians(angle))
-
-def cos_degrees(angle):
-    """Calculate the cosine of an angle in degrees."""
-    return math.cos(math.radians(angle))
-
-def tan_degrees(angle):
-    """Calculate the tangent of an angle in degrees."""
-    return math.tan(math.radians(angle))
-
-
-def inverse_trig_functions(value: float, function_name: str) -> str:
-    """
-    Calculates inverse trigonometric functions (asin, acos, atan) in degrees.
-
-    Args:
-        value: The value to calculate the inverse trigonometric function for.
-               For asin and acos, must be between -1 and 1.
-        function_name: "asin", "acos", or "atan".
-
-    Returns:
-        A string representing the result in degrees, or an error message.
-    """
-    if not isinstance(value, (int, float)):
-        return "Error: Input value must be a number."
-
-    func_name = function_name.lower()
-    result_rad = 0.0
-
-    if func_name == "asin":
-        if -1 <= value <= 1:
-            result_rad = math.asin(value)
-        else:
-            return "Error: Input for asin must be between -1 and 1."
-    elif func_name == "acos":
-        if -1 <= value <= 1:
-            result_rad = math.acos(value)
-        else:
-            return "Error: Input for acos must be between -1 and 1."
-    elif func_name == "atan":
-        result_rad = math.atan(value)
-    else:
-        return "Error: Invalid function name. Choose 'asin', 'acos', or 'atan'."
-
-    return f"{math.degrees(result_rad):.4f} degrees"
-
-
 def solve_trig_equations(a: float, b: float, c: float, trig_func: str, interval_degrees: tuple[float, float] = (0, 360)) -> str:
     """
     Solves basic trigonometric equations of the form a * func(x) + b = c.
     Finds solutions for x within a given interval (in degrees).
-
     Args:
         a: Coefficient of the trigonometric function.
         b: Constant term added to the function part.
         c: Constant term on the other side of the equation.
         trig_func: The trigonometric function ("sin", "cos", "tan").
         interval_degrees: Tuple (min_angle, max_angle) for solutions in degrees.
-
     Returns:
         A string describing the solutions in degrees.
     """
     if a == 0:
         return "Error: Coefficient 'a' cannot be zero."
-
-    # Rearrange to func(x) = (c - b) / a
     val = (c - b) / a
     func = trig_func.lower()
     solutions_deg = []
-
     if func == "sin":
         if not (-1 <= val <= 1):
             return f"No solution: sin(x) cannot be {val:.4f}."
@@ -87,19 +30,9 @@ def solve_trig_equations(a: float, b: float, c: float, trig_func: str, interval_
         angle_rad_principal = math.atan(val)
     else:
         return "Error: Invalid trigonometric function. Choose 'sin', 'cos', or 'tan'."
-
-    # Convert principal solution to degrees
     angle_deg_principal = math.degrees(angle_rad_principal)
-
     min_interval_deg, max_interval_deg = interval_degrees
-
-    # Find solutions within the interval
-    # General solutions:
-    # sin(x) = sin(alpha) => x = n*360 + alpha OR x = n*360 + (180 - alpha)
-    # cos(x) = cos(alpha) => x = n*360 + alpha OR x = n*360 - alpha
-    # tan(x) = tan(alpha) => x = n*180 + alpha
-
-    for n in range(int(min_interval_deg / 360) - 2, int(max_interval_deg / 360) + 3): # Check a few cycles around the interval
+    for n in range(int(min_interval_deg / 360) - 2, int(max_interval_deg / 360) + 3):
         if func == "sin":
             sol1_deg = n * 360 + angle_deg_principal
             sol2_deg = n * 360 + (180 - angle_deg_principal)
@@ -115,82 +48,11 @@ def solve_trig_equations(a: float, b: float, c: float, trig_func: str, interval_
             if min_interval_deg <= sol2_deg <= max_interval_deg:
                 solutions_deg.append(sol2_deg)
         elif func == "tan":
-            # For tan, general solution is n*180 + alpha
-             for n_tan in range(int(min_interval_deg / 180) - 2, int(max_interval_deg / 180) + 3):
+            for n_tan in range(int(min_interval_deg / 180) - 2, int(max_interval_deg / 180) + 3):
                 sol_deg = n_tan * 180 + angle_deg_principal
                 if min_interval_deg <= sol_deg <= max_interval_deg:
                     solutions_deg.append(sol_deg)
-
-    # Remove duplicates and sort
-    unique_solutions = sorted(list(set(f"{s:.2f}" for s in solutions_deg))) # Format to avoid floating point issues
-
+    unique_solutions = sorted(list(set(f"{s:.2f}" for s in solutions_deg)))
     if not unique_solutions:
         return f"No solutions found for {a}*{func}(x) + {b} = {c} in the interval [{min_interval_deg}, {max_interval_deg}] degrees."
-
     return f"Solutions for x in [{min_interval_deg}, {max_interval_deg}] degrees: {', '.join(unique_solutions)}"
-
-
-def trig_identities(angle_degrees: float, identity_name: str = "pythagorean1") -> str:
-    """
-    Demonstrates common trigonometric identities for a given angle (in degrees).
-
-    Args:
-        angle_degrees: The angle in degrees to evaluate the identities for.
-        identity_name: Name of the identity to demonstrate.
-                       "pythagorean1": sin^2(x) + cos^2(x) = 1
-                       "pythagorean2": 1 + tan^2(x) = sec^2(x)
-                       "pythagorean3": 1 + cot^2(x) = csc^2(x)
-                       "all": Show all Pythagorean identities.
-                       More can be added.
-
-    Returns:
-        A string demonstrating the identity.
-    """
-    x_rad = math.radians(angle_degrees)
-    sinx = math.sin(x_rad)
-    cosx = math.cos(x_rad)
-
-    # Avoid division by zero for tan, sec, cot, csc
-    # Check if cosx is very close to zero
-    if abs(cosx) < 1e-9: # cos(90), cos(270) etc.
-        tanx = float('inf') if sinx > 0 else float('-inf') if sinx < 0 else 0 # tan is undefined or 0 if sinx is also 0
-        secx = float('inf') if cosx >= 0 else float('-inf') # sec is undefined
-    else:
-        tanx = sinx / cosx
-        secx = 1 / cosx
-
-    # Check if sinx is very close to zero
-    if abs(sinx) < 1e-9: # sin(0), sin(180) etc.
-        cotx = float('inf') if cosx > 0 else float('-inf') if cosx < 0 else 0 # cot is undefined or 0 if cosx is also 0
-        cscx = float('inf') if sinx >= 0 else float('-inf') # csc is undefined
-    else:
-        cotx = cosx / sinx
-        cscx = 1 / sinx
-
-    results = []
-    name = identity_name.lower()
-
-    if name == "pythagorean1" or name == "all":
-        lhs = sinx**2 + cosx**2
-        results.append(f"Pythagorean Identity 1: sin^2({angle_degrees}) + cos^2({angle_degrees}) = {sinx**2:.4f} + {cosx**2:.4f} = {lhs:.4f} (Expected: 1)")
-
-    if name == "pythagorean2" or name == "all":
-        if abs(cosx) < 1e-9:
-             results.append(f"Pythagorean Identity 2 (1 + tan^2(x) = sec^2(x)): Not well-defined for x={angle_degrees} degrees as cos(x) is near zero (tan(x) and sec(x) are undefined or infinite).")
-        else:
-            lhs = 1 + tanx**2
-            rhs = secx**2
-            results.append(f"Pythagorean Identity 2: 1 + tan^2({angle_degrees}) = 1 + {tanx**2:.4f} = {lhs:.4f}. sec^2({angle_degrees}) = {secx**2:.4f}. (Expected LHS = RHS)")
-
-    if name == "pythagorean3" or name == "all":
-        if abs(sinx) < 1e-9:
-            results.append(f"Pythagorean Identity 3 (1 + cot^2(x) = csc^2(x)): Not well-defined for x={angle_degrees} degrees as sin(x) is near zero (cot(x) and csc(x) are undefined or infinite).")
-        else:
-            lhs = 1 + cotx**2
-            rhs = cscx**2
-            results.append(f"Pythagorean Identity 3: 1 + cot^2({angle_degrees}) = 1 + {cotx**2:.4f} = {lhs:.4f}. csc^2({angle_degrees}) = {cscx**2:.4f}. (Expected LHS = RHS)")
-
-    if not results:
-        return f"Unknown identity: {identity_name}. Available: pythagorean1, pythagorean2, pythagorean3, all."
-
-    return "\n".join(results)

maths/geometry/tan_degrees.py

@@ -0,0 +1,5 @@
+import math
+
+def tan_degrees(angle):
+    """Calculate the tangent of an angle in degrees."""
+    return math.tan(math.radians(angle))

maths/geometry/trig_identities.py

@@ -0,0 +1,53 @@
+import math
+
+def trig_identities(angle_degrees: float, identity_name: str = "pythagorean1") -> str:
+    """
+    Demonstrates common trigonometric identities for a given angle (in degrees).
+    Args:
+        angle_degrees: The angle in degrees to evaluate the identities for.
+        identity_name: Name of the identity to demonstrate.
+                       "pythagorean1": sin^2(x) + cos^2(x) = 1
+                       "pythagorean2": 1 + tan^2(x) = sec^2(x)
+                       "pythagorean3": 1 + cot^2(x) = csc^2(x)
+                       "all": Show all Pythagorean identities.
+                       More can be added.
+    Returns:
+        A string demonstrating the identity.
+    """
+    x_rad = math.radians(angle_degrees)
+    sinx = math.sin(x_rad)
+    cosx = math.cos(x_rad)
+    if abs(cosx) < 1e-9:
+        tanx = float('inf') if sinx > 0 else float('-inf') if sinx < 0 else 0
+        secx = float('inf') if cosx >= 0 else float('-inf')
+    else:
+        tanx = sinx / cosx
+        secx = 1 / cosx
+    if abs(sinx) < 1e-9:
+        cotx = float('inf') if cosx > 0 else float('-inf') if cosx < 0 else 0
+        cscx = float('inf') if sinx >= 0 else float('-inf')
+    else:
+        cotx = cosx / sinx
+        cscx = 1 / sinx
+    results = []
+    name = identity_name.lower()
+    if name == "pythagorean1" or name == "all":
+        lhs = sinx**2 + cosx**2
+        results.append(f"Pythagorean Identity 1: sin^2({angle_degrees}) + cos^2({angle_degrees}) = {sinx**2:.4f} + {cosx**2:.4f} = {lhs:.4f} (Expected: 1)")
+    if name == "pythagorean2" or name == "all":
+        if abs(cosx) < 1e-9:
+            results.append(f"Pythagorean Identity 2 (1 + tan^2(x) = sec^2(x)): Not well-defined for x={angle_degrees} degrees as cos(x) is near zero (tan(x) and sec(x) are undefined or infinite).")
+        else:
+            lhs = 1 + tanx**2
+            rhs = secx**2
+            results.append(f"Pythagorean Identity 2: 1 + tan^2({angle_degrees}) = 1 + {tanx**2:.4f} = {lhs:.4f}. sec^2({angle_degrees}) = {secx**2:.4f}. (Expected LHS = RHS)")
+    if name == "pythagorean3" or name == "all":
+        if abs(sinx) < 1e-9:
+            results.append(f"Pythagorean Identity 3 (1 + cot^2(x) = csc^2(x)): Not well-defined for x={angle_degrees} degrees as sin(x) is near zero (cot(x) and csc(x) are undefined or infinite).")
+        else:
+            lhs = 1 + cotx**2
+            rhs = cscx**2
+            results.append(f"Pythagorean Identity 3: 1 + cot^2({angle_degrees}) = 1 + {cotx**2:.4f} = {lhs:.4f}. csc^2({angle_degrees}) = {cscx**2:.4f}. (Expected LHS = RHS)")
+    if not results:
+        return f"Unknown identity: {identity_name}. Available: pythagorean1, pythagorean2, pythagorean3, all."
+    return "\n".join(results)

maths/geometry/trigonometry_interface.py

@@ -1,5 +1,10 @@
 import gradio as gr
-from maths.geometry.trigonometry import sin_degrees, cos_degrees, tan_degrees, inverse_trig_functions, solve_trig_equations, trig_identities
+from maths.geometry.sin_degrees import sin_degrees
+from maths.geometry.cos_degrees import cos_degrees
+from maths.geometry.tan_degrees import tan_degrees
+from maths.geometry.inverse_trig_functions import inverse_trig_functions
+from maths.geometry.solve_trig_equations import solve_trig_equations
+from maths.geometry.trig_identities import trig_identities
 
 # High School Math Tab
 trig_interface = gr.Interface(