Given the radius (r) of a sphere, an azimuth angle (angle around the vertical axis; s) and a polar angle (angle from horizontal; t) the equation to find the coordinates of the corresponding point is as follows:
x = r * cos(s) * sin(t)
y = r * cos(t)
z = r * sin(s) * sin(t)
This assumes the axes are in a Y-up right handed orientation.