Question

How do you evaluate `arccos(1/2)` without a calculator?

Answer 1

`60^@`

Explanation:

`arccos(1/2)` means give me the angle that gives a `cos(1/2)`.

If you look at a trig circle in the first quadrant, the angle with a `cos(1/2)` is `60^@`. This is found in the first quadrant because of the restricted domain and range of the function.

The graph of `f(x) = arccos(x)` has domain:`[-1,1]`, & range: `[0, pi]`
graph{arccos(x) [-5.687, 5.413, -1.287, 4.263]}