how to evaluate trig functions for common angles

Common angles for trig functions. They are quite easy.

Please take your time to remember this table. Just do it today.

$\theta$	$0$	$\frac{\pi }{6}$	$\frac{\pi }{4}$	$\frac{\pi }{3}$	$\frac{\pi }{2}$
$\sin (\theta )$	0	$\frac{1}{2}$	$\frac{\sqrt{2}}{2}$	$\frac{\sqrt{3}}{2}$	1
$\cos (\theta )$	1	$\frac{\sqrt{3}}{2}$	$\frac{\sqrt{2}}{2}$	$\frac{1}{2}$	0
$\tan (\theta )$	0	$\frac{1}{\sqrt{3}}$	1	$\sqrt{3}$	undefined

But if you forget, you can easily create this table anytime you wish, just use these steps.

$\theta$	$0$	$\frac{\pi }{6}$	$\frac{\pi }{4}$	$\frac{\pi }{3}$	$\frac{\pi }{2}$
$\sin (\theta )$	0	1	2	3	4
$\cos (\theta )$	4	3	2	1	0
$\tan (\theta )$

Then take their square roots and divide by two to get the table

$\theta$	$0$	$\frac{\pi }{6}$	$\frac{\pi }{4}$	$\frac{\pi }{3}$	$\frac{\pi }{2}$
$\sin (\theta )$	0	$\frac{1}{2}$	$\frac{\sqrt{2}}{2}$	$\frac{\sqrt{3}}{2}$	1
$\cos (\theta )$	1	$\frac{\sqrt{3}}{2}$	$\frac{\sqrt{2}}{2}$	$\frac{1}{2}$	0
$\tan (\theta )$	0	$\frac{1}{\sqrt{3}}$	1	$\sqrt{3}$	undefined