Sine of Integer Multiple of Pi

Theorem

Let $x \in \R$ be a real number.

Let $\sin x$ be the sine of $x$.

Then:

$\forall n \in \Z: \sin n \pi = 0$

Proof

This is established in Zeroes of Sine and Cosine.

$\blacksquare$

Also see

• Cosine of Integer Multiple of Pi