Please help with this question, please provide detailed working out for the subparts that is also legible, thanks!

Problem 1 Let R ~ Uniform(0, 1) and T ~ Uniform(-7, ") be independent random variables. Define a transformation from (R, T) to the new variables X = R cos T and Y = Rsin T. This is a smooth one-to-one transformation. 1 pts (a) What is the range of the transformation x = r cost, y = r sint (for t| 0? Why is this not the same as E[ X | T = 0] = ERT = 0 = E[R] = -, even though the events { Y = 0} and {7 = 0} are identical