Question

What is the inverse cosine of sqrt2/2?

Answer 1

`arccos(sqrt(2)/2)=pi/4`

Explanation:

"inverse cos" may also be written as `cos^(-1)` or "arccos"

If `arccos(sqrt(2)/2) = theta`

`rArrcolor(white)("XXX")cos(theta) = sqrt(2)/2`

This is a standard ratio for the angle `theta = pi/4`

Note: the inverse cosine is defined as having values restricted to the range `[0,pi)` and therefore `pi/4` is the only valid solution.