Therefore, what mathematicians traditionally consider a spherical coordinate system and what cartographers call a spherical coordinate system are somewhat different. There is no compelling reason why cartographers and mathematicians need to agree on the conventions involved. However, it is important for each to notice that formulas devised using one convention will probably not, without some modification, work in the other environment. Thus, if one attempts to mix the literature of these two disciplines, difficulties can easily arise. Thus, the distance coordinate usually represents elevation above the ellipsoid.
Cartographers use the plane of the equator as the reference point for latitude.
Mathematicians use the north pole. Cartographers would normally refer to the angle which mathematicians use as the co-latitude. A mathematician would probably say that Two Dimensional spherical is an oxymoron. There is no such thing as a two dimensional sphere. However, since cartographers concentrate their attention on a specific instance, i.e. a model of the earth, they have derived a special situation.