1. The problem statement, all variables and given/known data Suppose U follows a uniform distribution on the interval (0, 2pi). Find the density of sin(U) 2. Relevant equations 3. The attempt at a solution Well if U ~ (0, 2pi), then sin(U) should follow a distribution on [-1, 1]. I know one way to do tackle such problems is to let a be some element in [-1, 1] and then try to find [tex]P(sin(U) \leq a).[/tex] The big problem is that if I use this last expression, the next step seems to be to take the arcsin to get U is less than or equal to arcsin(a), but this seems ridiculous since we don't have monotonicity when dealing with the interval (0, 2pi). Is there another way to approach this problem?