Trigonometric Functions of Standard Angles

Theorem: Trigonometric Functions of Standard Angles

Here are some common values for sine, cosine, tangent and cotangent:

	$0$	$\frac{\pi }{6}$	$\frac{\pi }{4}$	$\frac{\pi }{3}$	$\frac{\pi }{2}$	$\frac{2\pi }{3}$	$\frac{5\pi }{6}$	$\pi$
$\sin \theta$	$0$	$\frac{1}{2}$	$\frac{\sqrt{2}}{2}$	$\frac{\sqrt{3}}{2}$	$1$	$\frac{\sqrt{3}}{2}$	$\frac{1}{2}$	$0$
$\cos \theta$	$1$	$\frac{\sqrt{3}}{2}$	$\frac{\sqrt{2}}{2}$	$\frac{1}{2}$	$0$	$-\frac{1}{2}$	$-\frac{\sqrt{3}}{2}$	$-1$
$\tan \theta$	$0$	$\frac{\sqrt{3}}{3}$	$1$	$\sqrt{3}$		$-\sqrt{3}$	$-\frac{\sqrt{3}}{3}$	$0$
$\cot \theta$		$\sqrt{3}$	$1$	$\frac{\sqrt{3}}{3}$	$0$	$-\frac{\sqrt{3}}{3}$	$-\sqrt{3}$

PROOF

TODO