Cylindrical parameterization

Question

Let S be the surface defined by the plane $$y+z=2$$ whose sides are the cylinder $$x^2+y^2 = 1$$Find the parameterization of the elliptical surface in cylindrical coordinates. Sorry about the non mathjax equations, but I'm kind of new here and I need some quick help.The problem as it appears on the sheet

Answer 1

Hint: the projection of the ellipse on the $XY$-plane is the (bidimensional) disk $x^2 + y^2\le 1$. You can parametrize the disk using polar coordinates. An the equation $y + z = 2$ gives the third coordinate.

Answer 2

Hint: $$\phi(\theta,z)=(\cos{\theta},\sin{\theta},2-\sin{\theta})$$