Question

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

Answer 1

Use a unit circle: `arccos(-1) = pi`

Explanation:

`arccos(-1)` means: find me the angle that gives a `cos(-1).`

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: `[-1, 1]` and Range: `[0, pi]`
graph{arccos(x) [-5.074, 4.79, -0.76, 4.172]}

This means that the only angle that has a `cos(-1) = pi`