Symmetry

What symmetry will you find in a surface that has an equation of the form in spherical coordinates? Please explain.

Answer: RADIAL symmetry. Notice that represents the "radius" at that point on the 3D figure, and represents the angle off the "north pole" and nowhere in the function is mentioned. Therefore, the function will have the same value regardless of , so you can rotate it about the z-axis without changing it's shape, therefore, you have radial symmetry.