Special Angles

Drag a point to a random angle like 37° and sin gives an ugly decimal — 0.602. Fine. But a few angles give exact, beautiful values: ½, √2⁄2, √3⁄2. They're not luck. They come from two triangles so symmetric that the math collapses — the 45-45-90 (half a square) and the 30-60-90 (half an equilateral triangle).