You are working with the sphere [tex]x^2+ y^2+ z^2= 2z[/itex], a sphere of radius 1, centered at (0, 0, 1). In spherical coordinates, $\displaystyle x= \rho cos(\theta)sin(\phi)$, $\displaystyle y= \rho sin(\theta)sin(\phi)$, $\displaystyle z= \rho cos(\theta)$. Since the radius of the sphere is 1, $\displaystyle \rho= 1$ and we have $\displaystyle x^2+ y^2+ z^2= 1$ and $\displaystyle 2z= 2cos(\phi)$.