CST

import math

def analyze_divisible_angles():
    """
    Analyzes angles divisible by 3 up to 90°, comparing a custom pattern
    to trigonometric functions (cosine, sine, tangent).
    """
    print("# Analysis of Angles and Trigonometric Patterns")
    print("\nAngle | Third | Pattern | cos(θ) | sin(θ) | tan(θ) | Diff (cos) | Diff (sin) | Diff (tan)")
    print("------|-------|---------|--------|--------|--------|------------|------------|------------")

    bool_div = -1  # Initialize pattern multiplier

    for angle in range(1, 91, 1):
        third = angle / 3  # Exact third of the angle
        angle_rad = math.radians(angle)

        # Trigonometric functions
        cos_val = math.cos(angle_rad)
        sin_val = math.sin(angle_rad)
        tan_val = math.tan(angle_rad) if angle != 90 else float('inf')  # Avoid infinity at 90°

        # Compute pattern
        x_recip = 1 / (angle if angle != 0 else 1)  # Reciprocal of angle
        max_val = max(angle, x_recip)
        min_val = min(angle, x_recip)
        pattern = math.radians(-1 * (max_val - min_val - max_val))

        # Toggle `bool_div` every 3rd angle
        if angle % 3 == 0:
            bool_div *= 1

        # Compute differences
        diff_cos = abs(pattern - cos_val)
        diff_sin = (abs(pattern / angle)) # if sin_val != 0 else (abs(pattern - (1 / sin_val)))
        diff_tan = abs(pattern)**2/3

#        print(f"{angle:3d}° | {third:5.1f}° | {pattern:8.4f} | {cos_val:6.4f} | {sin_val:6.4f} | {tan_val:6.4f} | {diff_cos:10.6f} | {diff_sin:10.6f} | {diff_tan:10.6f}")

        # Highlight small differences
        if diff_cos < 0.1 or diff_sin < 0.1 or diff_tan < 0.1:
            print(f"\n🔹 Significant match at {angle}°:")
            print(f"   - Pattern: {pattern:.6f}")
            print(f"   - cos(θ): {cos_val:.6f}, sin(θ): {sin_val:.6f}, tan(θ): {tan_val:.6f}")
            print(f"   - Diff (cos): {diff_cos:.6f}, Diff (sin): {diff_sin:.6f}, Diff (tan): {diff_tan:.6f}")
            print("---")

# Run the function
analyze_divisible_angles()