As you can guess, this is a polar change of coordinates. You can show that and .The second part of the problem:
Let the transformation from (X,Y) -> (R,θ) be defined as
find the joint density and marginal densities.
So far on this part I have it solved for X and Y:
I tried plugging in the equations into each other but I don't know how to get rid of the tan(). Any help is appreciated.
For instance, you can write , square this equation and deduce the expression for (using at the end, and ).