Some hints:
To find the inverse function what do you reflect y=cos(x) in?
and for the inverse to exist it must be 1 to 1.
This wording is ambiguous, depending on whether you denote the inverse cosine function as "cos inverse" or "inverse cos". I suspect that the OP and Mr F are interpreting it in opposite ways. So, starting from x, do you apply the cosine first, and then the inverse, or is it the other way round?