I know what the graph of:
y=cos^-1(cos(x))
looks like.
However, can someone explain to me how you would know how to sketch it without simply subbing in values to get points. Something about restrictions and how it is a periodic function possibly?
Are you sure you know what the function looks like?
The angle whose cosine is cosine x, is x itself. That is what cos^-1(cos(x)) means.
It should be easy to plot. It isn't even periodic! However, the cos^-1 function is multiple valued. If you add 2 pi n to x, with n an integer, you get the same value of the cosine