# What are the exact values of cos 150° and sin 150°?

May 16, 2018

$\cos \left(150\right) = - \frac{\sqrt{3}}{2}$
$\sin \left(150\right) = \frac{1}{2}$

#### Explanation:

First of all, observe that $150 = 180 - 30$.

Then, remember that we have

$\cos \left(180 - x\right) = - \cos \left(x\right)$
$\sin \left(180 - x\right) = \sin \left(x\right)$

Plug in $x = 30$ to get

$\cos \left(180 - 30\right) = - \cos \left(30\right)$
$\sin \left(180 - 30\right) = \sin \left(30\right)$

the answer comes from the fact that $\cos \left(30\right) = \frac{\sqrt{3}}{2}$ and $\sin \left(30\right) = \frac{1}{2}$ are known values.