Trigonometry: The Math of Circles and Waves

Trigonometry is not 'memorize SOH CAH TOA.' It is the math of anything that repeats: sound waves, seasons, rotations, heartbeats. This guide starts from a point moving around a circle and builds up to the sine, cosine, and tangent that power graphics, audio, and animation.

1. The Unit Circle and Why Sine/Cosine Exist Trigonometry starts with a point moving around a circle. The height of that point is sine. The horizontal position is cosine. This phase explains why those functions exist, how to read the unit circle, and why radians are the natural way to measure angles.
2. Waves, Frequencies, and the Real World A sine wave is the shape of every repeating phenomenon: sound, light, seasons, heartbeats. This phase shows how amplitude, frequency, and phase shift turn a single circle into the full language of waves, and how to generate a simple audio tone with code.
3. Rotation, Navigation, and Where Am I Facing Trigonometry is the math of direction. Rotating a sprite, pointing a camera, triangulating a position: all of them use sine and cosine to turn an angle into a coordinate. This phase connects the circle to the graphics, audio, and navigation systems you use every day.