Mathematica gives you the power to visualize functions of two variables in multiple ways, including three-dimensional parametric plots, spherical polar plots, revolution plots, and contour plots.
Use
ParametricPlot3D to plot the surface defined by

:
Create a polar plot of a sphere of unit radius:
Generate a plot of the surface of revolution of the curve

:
Use
ContourPlot3D to plot a function implicitly defined by

: