# How do you evaluate arccos(-1) without a calculator?

Feb 18, 2017

Use a unit circle: $\arccos \left(- 1\right) = \pi$

#### Explanation:

$\arccos \left(- 1\right)$ means: find me the angle that gives a $\cos \left(- 1\right) .$

You do need to realize that the $\arccos$ function has a restricted domain and range.

From the graph you can see that the restrictions are as follows:
Domain: $\left[- 1 , 1\right]$ and Range: $\left[0 , \pi\right]$
graph{arccos(x) [-5.074, 4.79, -0.76, 4.172]}

This means that the only angle that has a $\cos \left(- 1\right) = \pi$