# How do you find the exact value of arccos (-sqrt3/2)?

Oct 6, 2016

The angle whose cosine is $\left(- \frac{\sqrt{3}}{2}\right)$ is 150 degrees or $\frac{5}{6} \pi$

#### Explanation:

Draw an equilateral triangle.
Cut it in half .
The angles in this right angle triangle are 30 ,60, 90
If the hypotenuse is length 2 then the shortest side is 1 and from Pythagoras the other side is $\sqrt{3}$
So the angle whose cosine is $\frac{\sqrt{3}}{2}$ is 30 degrees.
Now sketch the cosine graph.
From this you can find the angle whose cosine is $\left(- \frac{\sqrt{3}}{2}\right)$
Is 150 degrees or $\frac{5}{6} \pi$