# Trigonometry with Sin & Cos

**Track:** Foundations — Creative Coding — the existing 50
**Framework / surface:** p5.js
**Level:** Intermediate
**Prerequisites:** Animation & the Frame Loop, Transformations & the Matrix Stack

**In one line:** Turn an angle into coordinates — the circle-and-wave math behind smooth motion.

## Theory, aesthetics & inspiration

Sine and cosine convert an angle into a pair of coordinates: a point traveling around the unit circle traces cosine on one axis and sine on the other, so circular motion and the wave become the same fact seen two ways. These periodic functions are the mathematics of everything that cycles — orbits, oscillations, breathing rhythms. Jules Antoine Lissajous's nineteenth-century figures, drawn by coupling two such oscillations, and John Whitney's harmonic computer films both show their visual fertility. For an artist, sin and cos are the shortest path from rigid grids to organic motion: smooth easing, pendular sway, spirals and ripples all fall out of feeding a steadily increasing angle into these two curves.