# Cosine of Multiple of Pi Plus Half

## Theorem

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

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

Then:

$\forall n \in \Z: \cos \left({n + \dfrac 1 2}\right) \pi = 0$

## Proof

This is established in Zeroes of Sine and Cosine.

$\blacksquare$