# Sine of Angle plus Straight Angle

## Theorem

$\map \sin {x + \pi} = -\sin x$

## Proof

 $\ds \map \sin {x + \pi}$ $=$ $\ds \sin x \cos \pi + \cos x \sin \pi$ Sine of Sum $\ds$ $=$ $\ds \sin x \cdot \paren {-1} + \cos x \cdot 0$ Cosine of Straight Angle and Sine of Straight Angle $\ds$ $=$ $\ds -\sin x$

$\blacksquare$