Okay. Let .so the problem is: f(x) = sin(arctan(x)). Find f-1(1/2).

So we have . The idea is to isolate x and have it in function of y. The x variable is affected by arctan and also by sin. But as sin also affects arctan, we should start "taking it off" first. We can rewrite the equation into the following one which is equivalent : . Now taking off the arctan affecting x : . Done, since is precisely . Just evaluate this function with .