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Re: spherical geometry

I am trying to address Carl's problem in my own way but I need help.

Consider a point A located on a sphere of unit radius. The polar axis
of the sphere, z on my picture, is vertical. The two spherical
coordinates of A are TET (polar angle) and PHI (azimuthal angle).

Another polar axis, z', is chosen. Its orientation, in the old frame,
is specified by ALPHA (polar) and BETA (azimuthal). How are new polar
coordinates, TET' and PHI', expressed in terms of old polar
coordinates? I realize that the transformation is not as simple as for
xy and x'y'.

Ludwik Kowalski