Answered
There's a direct conversion from a given cartesian triple (x, y, z) to spherical coordinates (rho, angle theta, angle phi). In theory angle phi is the angle (rho, z axis) but it seems that the automatic conversion gives the complement of angle phi.
Was I thinking wrongly or is it a bug? Please illuminate me. Thanks.
The same question 
For phi there are two traditions and e.g. mathematics, physics and geography don't always tend to the same choice. So GeoGebra had to chose one of both.
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