Write the equation $x^2+y^2=2y$ in spherical coordinates.
My solution: Using relation between spherical coordinates and rectangular we get:$$(\rho \cos \theta \sin \phi)^2+(\rho \sin \theta \sin \phi)^2=2\rho \sin \theta \sin \phi$$ $$\rho^2 \sin^2 \phi=2\rho \sin \theta \sin \phi$$
However the answer on the book is $\rho \sin \phi=2\sin \theta$. It look like mine but after reduction to $\rho \sin \phi$. Can anyone explain why we can reduce above equation to $\rho \sin \phi$? What about $\rho=0$ and $\phi=0,\pi$?
Would be very grateful for good explanation.