Trigonometric Identities for Argument Offsets

Theorem: Trigonometric Identities for Argument Offsets

The sine, cosine, tangent and cotangent have the following properties:

	$\frac{\pi }{2}+\theta$	$\frac{\pi }{2}-\theta$	$\pi +\theta$	$\pi -\theta$	$\frac{3\pi }{2}+\theta$	$\frac{3\pi }{2}-\theta$
$\sin$	$\cos \theta$	$\cos \theta$	$-\sin \theta$	$\sin \theta$	$-\cos \theta$	$-\cos \theta$
$\cos$	$-\sin \theta$	$\sin \theta$	$-\cos \theta$	$-\cos \theta$	$\sin \theta$	$-\sin \theta$
$\tan$	$-\cot \theta$	$\cot \theta$	$\tan \theta$	$-\tan \theta$	$-\cot \theta$	$\cot \theta$
$\cot$	$-\tan \theta$	$\tan \theta$	$\cot \theta$	$-\cot \theta$	$-\tan \theta$	$\tan \theta$

PROOF

TODO