Question

What is the Inverse cos(cos(-pi/3)?

Answer 1

`arccos(cos(-pi/3)) = pi/3`

Explanation:

In order that `arccos` be a well-defined function, its range is defined to be `[0, pi]`.

So if `theta = arccos(cos(-pi/3))`, then `cos(theta) = cos(-pi/3)` and `theta in [0, pi]`

For any `theta` we have `cos(theta) = cos(-theta)`, so we can see that in our case `theta = pi/3` satisfies the required conditions to be `arccos(cos(-pi/3))`

Here's the graph of `arccos(theta)`

graph{arccos(x) [-5.168, 4.83, -0.86, 4.14]}