# Cosine of Angle plus Right Angle

## Theorem

$\map \cos {x + \dfrac \pi 2} = -\sin x$

## Proof

 $\displaystyle \map \cos {x + \frac \pi 2}$ $=$ $\displaystyle \cos x \cos \frac \pi 2 - \sin x \sin \frac \pi 2$ Cosine of Sum $\displaystyle$ $=$ $\displaystyle \cos x \cdot 0 - \sin x \cdot 1$ Cosine of Right Angle and Sine of Right Angle $\displaystyle$ $=$ $\displaystyle -\sin x$

$\blacksquare$