Euler's formula - Aetherwisp

Euler's formula is an equation in complex analysis that allows one to convert between trigonometric functions and complex exponentials. It states

e^{i\theta}=\sin \theta+i\cos \theta

When $\theta=\pi$ , it takes on a form known as Euler's identity:

e^{i\pi}=-1

This formula can be used to rewrite the sine and cosine as complex functions:

\sin \theta=\frac{e^{i\theta}-e^{-i\theta}}{2i},\qquad \cos \theta=\frac{e^{i\theta}+e^{-i\theta}}{2}