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-axis and the position vector of k.

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