There are good dicussions of spherical coordinates in wikipedia spherical coordinate system and Mathworld spherical coordinate system.
There is more information in the docstring for the sphere2cart() function.
The radius is r, the inclination angle is \theta and the azimuth angle is \phi. Spherical coordinates are specified by the tuple of (r, \theta, \phi) in that order.
Here is a good illustration we made from the scripts kindly provided by Jorge Stolfi on wikipedia.
The formulae relating Cartesian coordinates (x, y, z) to r, \theta, \phi are:
r=\sqrt{x^2+y^2+z^2} \theta=\arccos\frac{z}{\sqrt{x^2+y^2+z^2}} \phi = \operatorname{atan2}(y,x)
and from (r, \theta, \phi) to (x, y, z):
x=r \, \sin\theta \, \cos\phi y=r \, \sin\theta \, \sin\phi z=r \, \cos\theta
See wikipedia spherical coordinate system . The mathematics convention reverses the meaning of \theta and \phi so that \theta refers to the azimuthal angle and \phi refers to the inclination angle.
Matlab has functions sph2cart and cart2sph. These use the terms theta and phi, but with a different meaning again from the standard physics and mathematics conventions. Here theta is the azimuth angle, as for the mathematics convention, but phi is the angle between the reference plane and OP. This implies different formulae for the conversions between Cartesian and spherical coordinates that are easy to derive.