Euler’s formula for sine

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

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

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

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

Sine is the yellow dot, the vector sum of green and pink.

Just music, no narration. The background music is Book Bag by E’s Jammy Jams.

Animated with d3.js, source code.

Created by Willy McAllister.