Question

How do you evaluate `cos^-1(cos((pi)/10))`?

Answer 1

The answer is `pi/10`

Explanation:

By definition, `cos^(-1)(x)` is an angle `phi` that satisfies two requirements:

(1) `cos phi = x` (the main part of a definition)

(2) `0<=phi<=pi` (to assure uniqueness of the result)

In our case `x=cos(pi/10)`, so the first requirement is `cos(phi)=cos(pi/10)` and the obvious candidate for `phi` is `pi/10`.

For this `phi=pi/10` the second requirement is held.

Therefore, the answer is `pi/10`.