# Trigonometry/e to the i Pi

Take the formula

${\displaystyle e^{xi}=\cos(x)+i\sin(x)}$ .

If ${\displaystyle x=\pi }$ radians, ${\displaystyle \cos(x)=-1}$ and ${\displaystyle \sin(x)=0}$ so the formula becomes

${\displaystyle e^{\pi i}=-1}$

or

${\displaystyle e^{\pi i}+1=0}$

a formula relating five key numbers in mathematics.