# Cosine of Straight Angle

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## Theorem

$\cos 180^\circ = \cos \pi = - 1$

where $\cos$ denotes cosine.

## Proof

A direct implementation of Cosine of Multiple of Pi:

$\forall n \in \Z: \cos n \pi = \paren {-1}^n$

In this case, $n = 1$ and so:

$\cos \pi = -1^1 = -1$

$\blacksquare$