Choose a point k uniformly at random from the following set {(x,y):y>0,x^2+y^2<1}. Set Z the angle between the x-axes and the position vector of k.

1. Find the cumulative distribution function of Z.
2. Find the probability density function of Z.
3. Find expectation of Z.
4. Find Var(Z).
5. Find E[sin(Z)]
6. Find the third moment.