Question

How do you evaluate `arccos{cos(pi/3)}`?

Answer 1

`pi/3`

Explanation:

cos and arc cos are inverse operators.

For any inverse operator couple `[O, O^(-1)]`,

`O(O^(-1)x) = x and O^(-1)(Oy)=y`.

Here, `arc cos (cos (pi/3))=pi/3`

Despite `cos(pi/3)=1/2=cos(-pi/3)`,.

`arc cos(cos(-pi/3))=-pi/3`, and not `pi/3.`.