Create Trigonometric_Identity_Animation.py

Author: sksalahuddin2828

Trigonometric_Identity_Animation.py

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+import sympy as sp
+import numpy as np
+import matplotlib.pyplot as plt
+from mpl_toolkits.mplot3d import Axes3D
+
+# Define symbols
+alpha, beta = sp.symbols('alpha beta')
+
+# Define the identity
+lhs = sp.cos(alpha + beta)
+rhs = sp.cos(alpha) * sp.cos(beta) - sp.sin(alpha) * sp.sin(beta)
+
+# Check if the identity holds true
+identity_holds = sp.simplify(lhs - rhs) == 0
+print("Does the identity hold true?", identity_holds)
+
+# Create 3D plot for visualization
+alpha_vals = np.linspace(0, 2 * np.pi, 100)
+beta_vals = np.linspace(0, 2 * np.pi, 100)
+alpha_vals, beta_vals = np.meshgrid(alpha_vals, beta_vals)
+
+lhs_vals = np.cos(alpha_vals + beta_vals)
+rhs_vals = np.cos(alpha_vals) * np.cos(beta_vals) - np.sin(alpha_vals) * np.sin(beta_vals)
+
+fig = plt.figure()
+ax = fig.add_subplot(111, projection='3d')
+ax.plot_surface(alpha_vals, beta_vals, lhs_vals, cmap='coolwarm', label='lhs')
+ax.plot_surface(alpha_vals, beta_vals, rhs_vals, cmap='viridis', label='rhs')
+
+ax.set_xlabel('Alpha')
+ax.set_ylabel('Beta')
+ax.set_zlabel('Value')
+ax.set_title('Trigonometric Identity: cos(α±β) = cosαcosβ ∓ sinαsinβ')
+
+from matplotlib.animation import FuncAnimation
+
+fig = plt.figure()
+ax = fig.add_subplot(111, projection='3d')
+
+def update(frame):
+    ax.cla()  # Clear the previous frame
+    new_alpha = alpha_vals + frame * 0.1
+    new_lhs = np.cos(new_alpha + beta_vals)
+    new_rhs = np.cos(new_alpha) * np.cos(beta_vals) - np.sin(new_alpha) * np.sin(beta_vals)
+    ax.plot_surface(alpha_vals, beta_vals, new_lhs, cmap='coolwarm', label='lhs')
+    ax.plot_surface(alpha_vals, beta_vals, new_rhs, cmap='viridis', label='rhs')
+    ax.set_xlabel('Alpha')
+    ax.set_ylabel('Beta')
+    ax.set_zlabel('Value')
+    ax.set_title('Trigonometric Identity Animation')
+    ax.legend()
+
+ani = FuncAnimation(fig, update, frames=50, interval=100)
+plt.show()