1. The problem statement, all variables and given/known data From an old edition of the Anton calculus text, I am asked to prove cos-1(-x) + cos-1(x) = π or equivalently cos-1(-x) = π - cos-1(x) 2. Relevant equations 3. The attempt at a solution Earlier I proved that sin-1(x) was odd by noting sin-1(sin(x)) = -sin-1(sin(-x)), so I have tried to start the problem from the same approach, but none of my attempts have been insightful. I started with cos-1(cos(x)) = x and cos-1(cos(-x)) = -x but I am not going anywhere with it. I'm stuck. It makes geometric sense that the sum cos-1(-x) + cos-1(x) is in fact π when viewing a graph of cos-1(x). But how do I prove this one? It appears that I am not supposed to use derivatives of the inverses to solve this (they are covered after this section in the text). It is from Anton's Brief Edition 1981, p 462. Any hints or the like are appreciated.