Sine and Cosine of Angle plus Integer Multiple of Pi

Theorem

For $n \in \Z, \theta \in \R$:

Cosine of Angle plus Integer Multiple of Pi

$\map \cos {\theta + n \pi} = \paren {-1}^n \cos \theta$

Sine of Angle plus Integer Multiple of Pi

$\map \sin {\theta + n \pi} = \paren {-1}^n \sin \theta$