So I have f(x)= arccos(cos(x)). When I graphed it on a graphing calculator I see that the f(x) is never lower then 0. So is there an explanation for this?.

Answer 1

The "angle whose cosine is cosine x" is any angle at all.

If you let x represent any angle, it's cosine will be cos x and the angle that has that cosine can be x OR -x, because of the symmetry of the cos x function, which is even. The computer will select the positive value, no matter which sign x has.

That's a very interesting question.