I'm confused by (what appears to be) a discrepancy concerning the range assumptions for the spherical coordinate system.
The following command tells Mathematica to report the range assumptions for its spherical coordinate system:
Mathematica then reports:
a > 0 && 0 < b < Pi && -Pi < c <= Pi
That is at odds with the description given in Wolfram's Mathworld
Unlike the above report from Mathematica, Mathworld describes the range as: