unit circle

in trigonometry, the unit circle has the equation $x^2+y^2=1$

figure: the unit circle graphed

the unit circle is useful in trigonometry because it visualizes the outputs of the trig functions given an angle $\theta$

by the way when we measure angles, we use either degrees or radians. if an angle has no units, it’s in radians

for how to evaluate the sine and cosine, see how to evaluate trig functions

here are just some more values you should ignore

radians	degrees	cos - x value	sin - y value
0	0	1	0
$\frac{1}{6}\pi$	30	$\frac{\sqrt{3}}{2}$	$\frac{1}{2}$
$\frac{1}{4}\pi$	45	$\frac{\sqrt{2}}{2}$	$\frac{\sqrt{2}}{2}$
$\frac{1}{3}\pi$	60	$\frac{1}{2}$	$\frac{\sqrt{3}}{2}$
$\frac{1}{2}\pi$	90	0	1
$\frac{2}{3}\pi$	120	$\frac{-1}{2}$	$\frac{\sqrt{3}}{2}$
$\frac{3}{4}\pi$	135	$-\frac{\sqrt{2}}{2}$	$\frac{\sqrt{2}}{2}$
$\frac{5}{6}\pi$	150	$\frac{-\sqrt{3}}{2}$	$\frac{1}{2}$
$\pi$	180	-1	0
$\frac{5}{4}\pi$	225	$-\frac{\sqrt{2}}{2}$	$-\frac{\sqrt{2}}{2}$
$\frac{6}{4}\pi$	270	0	-1
$\frac{7}{6}\pi$	210	$\frac{-\sqrt{3}}{2}$	$\frac{-1}{2}$
$\frac{7}{2}\pi$	315	$\frac{\sqrt{2}}{2}$	$-\frac{\sqrt{2}}{2}$
$\frac{4}{3}\pi$	240	$\frac{-1}{2}$	$\frac{-\sqrt{3}}{2}$
$\frac{9}{4}\pi$	360	1	0