# Sine of Angle plus Straight Angle

 It has been suggested that this page or section be merged into Sine and Cosine are Periodic on Reals/Corollary. (Discuss)

## Theorem

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

## Proof

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

$\blacksquare$