Euler’s formula for cosine

$\cos \omega t = \dfrac{1}{2} (e^{+j\omega t} + e^{-j\omega t})$

A cosine emerges from spinning numbers in Euler’s Formula,

The spinning green vector is $\dfrac{1}{2} e^{+j\omega t}$

The spinning red vector is $+\dfrac{1}{2} e^{-j\omega t}$

Cosine is the orange dot, the vector sum of green and red.

Just music, no narration. The background music is NirvanaVEVO by Chris Zabriskie.

Animated with d3.js, source code.

Created by Willy McAllister.