Sine of Angle plus Straight Angle

From ProofWiki
Jump to navigation Jump to search

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
\(\displaystyle \) \(=\) \(\displaystyle -\sin x\)

$\blacksquare$


Also see


Sources