feat: enhance Gradio interfaces for trigonometric functions with detailed descriptions and examples

maths/geometry/cos_degrees.py

@@ -10,5 +10,6 @@ cos_degrees_interface = gr.Interface(
     inputs=gr.Number(label="Angle (degrees)"),
     outputs="number",
     title="Cosine Calculator",
-    description="Calculate cosine of an angle in degrees."
+    description="Calculate the cosine of an angle in degrees. Enter an angle (e.g., 60) to get its cosine value.",
+    examples=[[0], [60], [90], [180]]
 )

maths/geometry/inverse_trig_functions.py

@@ -39,5 +39,11 @@ inverse_trig_interface = gr.Interface(
     ],
     outputs="text",
     title="Inverse Trigonometry Calculator",
-    description="Calculate inverse trigonometric functions. Output in degrees."
+    description="Calculate inverse trigonometric functions (asin, acos, atan) and get the result in degrees. For asin and acos, input must be between -1 and 1. Example: asin(0.5) = 30 degrees.",
+    examples=[
+        [0.5, "asin"],
+        [0.5, "acos"],
+        [1, "atan"],
+        [-1, "asin"]
+    ]
 )

maths/geometry/sin_degrees.py

@@ -10,5 +10,6 @@ sin_degrees_interface = gr.Interface(
     inputs=gr.Number(label="Angle (degrees)"),
     outputs="number",
     title="Sine Calculator",
-    description="Calculate sine of an angle in degrees."
+    description="Calculate the sine of an angle in degrees. Enter an angle (e.g., 30) to get its sine value.",
+    examples=[[0], [30], [45], [90]]
 )

maths/geometry/solve_trig_equations.py

@@ -78,5 +78,11 @@ solve_trig_equations_interface = gr.Interface(
     ],
     outputs="text",
     title="Trigonometric Equation Solver",
-    description="Solves equations like a * func(x) + b = c for x in a given interval (degrees)."
+    description="Solves equations like a * func(x) + b = c for x in a given interval (degrees). Enter the coefficients, select the function, and specify the interval for x. Example: Solve 2*sin(x) + 1 = 1 for x in [0,360] degrees.",
+    examples=[
+        [2, 1, 1, "sin", "0,360"],
+        [1, 0, 0.5, "cos", "0,360"],
+        [1, 0, 1, "tan", "0,360"],
+        [1, 0, 2, "sin", "0,360"]
+    ]
 )

maths/geometry/tan_degrees.py

@@ -10,5 +10,6 @@ tan_degrees_interface = gr.Interface(
     inputs=gr.Number(label="Angle (degrees)"),
     outputs="number",
     title="Tangent Calculator",
-    description="Calculate tangent of an angle in degrees."
+    description="Calculate the tangent of an angle in degrees. Enter an angle (e.g., 45) to get its tangent value.",
+    examples=[[0], [45], [60], [90]]
 )

maths/geometry/trig_identities.py

@@ -69,5 +69,11 @@ trig_identities_interface = gr.Interface(
     ],
     outputs="text",
     title="Trigonometric Identities Demonstrator",
-    description="Show common trigonometric identities for a given angle."
+    description="Show common trigonometric identities for a given angle. Select an identity and enter an angle (e.g., 45) to see the identity demonstrated with calculated values.",
+    examples=[
+        [45, "pythagorean1"],
+        [60, "pythagorean2"],
+        [30, "pythagorean3"],
+        [90, "all"]
+    ]
 )