Euler’s formula for cosine

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

Cosine emerges on the real axis, the vector sum of two spinning numbers,

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 (the orange dot) is the vector sum of green and red.

Created by Willy McAllister.

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

Animated with d3.js, source code.