# Cosine of Half-Integer Multiple of Pi

## Theorem

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

Let $\cos x$ denote the cosine of $x$.

Then:

$\forall n \in \Z: \map \cos {n + \dfrac 1 2} \pi = 0$

## Proof

This is established in Zeroes of Sine and Cosine.

$\blacksquare$