For some specific reasons, I need to use an alternative spherical coordinate system defined as follows:
$x=R~{\rm cos}~\varphi~{\rm cos}~\vartheta, \\ y=R~{\rm sin}~\varphi, \\ z=-R~{\rm cos}~\varphi~{\rm sin}~\vartheta,$
where $R \ge 0$, $\vartheta \in [0, \pi)$, and $\varphi \in [0, 2\pi)$.
My question is whether there is a standard name for this coordinate system. If no, how would you call this system?