1. The problem statement, all variables and given/known data The problem here involves inverse trig functions. The question here is why doesn't arccos(cos x) yield the equation y = x? 2. Relevant equations y = arccos(cos x) 3. The attempt at a solution I assume the reason is due to restrictions on domain and/or range of the trig functions. I graphed it out from -4pi to 4pi, and noticed that from 0 to pi, 2pi to 3pi, etc., it does display a function similar y = x (0 to pi it IS y = x). However, on intervals such as -pi to 0, it is the same as the function y = -x. Now, I looked at the unit circle and can see that, if it is the arccos (cos x), the cos of radian measurements (essentially the sine when reading on the unit circle) is strictly positive. However, between -pi and 0, the values would be negative. They increase and decrease graphically, respectively. Anyone have any input or guiding suggestions here? Thanks.