I know that to find the implied domain of y=arcsin(cos(x)) one must first find the domain of arcsin and then set up an inequation and solve for x. For this particular example: cos(x) is less than or equal to 1 and greater than or equal to -1. However, when you have an equation such as y=arctan(cos(x)) and you take the domain of arctan you end up with all real numbers.
My question then is this: how does one find the implied domain of an equation of this kind using this method, given that you can't take the inverse cos of R to solve for x?
Or, alternatively, is there a more effective way of approaching these kinds of problems?