# Cosine of 315 Degrees

## Theorem

$\cos 315 \degrees = \cos \dfrac {7 \pi} 4 = \dfrac {\sqrt 2} 2$

where $\cos$ denotes cosine.

## Proof

 $\ds \cos 315 \degrees$ $=$ $\ds \map \cos {360 \degrees - 45 \degrees}$ $\ds$ $=$ $\ds \cos 45 \degrees$ Cosine of Conjugate Angle $\ds$ $=$ $\ds \frac {\sqrt 2} 2$ Cosine of $45 \degrees$

$\blacksquare$