I have the following problem.
Let X be a random variable uniformly distributed on $[-1,1]$ and let be $Y=cos(X)$.
a) Find the function of density and distribution of Y
b) Find the espectation of Y ,E(Y).
For a), I put the following;
Let G be the function of distribution of Y, then
$$G(y)=P(Y\leq y)=P(cos(X)\leq y)$$
But from here I don't know how to proceed! This is because cos is nos strictly inceasing or decreasing functon and I dont have any idea about how to use arccos function.
Any help would be appreciated.