I just can't see what's wrong, this should be relatively simple...
I have a vector which has length 1. Then, I have two angles. The first ($\gamma$) is the angle between the projection of the vector in the $xz$ plane and the $z$ axis. The second ($\beta$) is the angle between the projection of the vector in the $yz$ plane and the $z$ axis.
All I need now are the (cartesian) vector components $(x,y,z)$.
How do I calculate them?
I got: $x = \sin(\gamma)\\ y = \sin(\beta)\\ z = \cos(\gamma) \cdot \cos(\beta)$
But this can't be correct, because the length of this vector is not always 1. Can you help me and find the error, please?