# Euler Formula for Sine Function

## Theorem

### Real Numbers

$\displaystyle \sin x = x \prod_{n \mathop = 1}^\infty \paren {1 - \frac {x^2} {n^2 \pi^2} }$

for all $x \in \R$.

### Complex Numbers

$\displaystyle \sin z = z \prod_{n \mathop = 1}^\infty \left({1 - \frac {z^2} {n^2 \pi^2}}\right)$

for all $z \in \C$.

## Source of Name

This entry was named for Leonhard Paul Euler.

## Historical Note

The Euler Formula for Sine Function was not put on an adequately rigorous footing until Karl Weierstrass provided a satisfactory proof for Weierstrass Factor Theorem.