Hey everyone. I'm having trouble understanding this example. It says,

Find the inverse of

, so

So far everything is straightforward. Then the solution says:

From the trigonometric formula with and , we obtain

Okay. If I plug x and y into the given trig formula, it comes out as the integral above. However,

and

I'm confused to how/why they did that because it doesn't make sense (at least not to me).

Any help is appreciated. Thanks in advance!