Azimuthal angle in cylindrical coordinates ($\varphi$)

The azimuthal angle $\varphi$ in cylindrical coordinates is measured in the horizontal plane from a chosen reference axis. In the usual mathematical convention $x=s\cos \varphi$, $y=s\sin \varphi$, so positive $\varphi$ runs counterclockwise from positive $x$ when viewed from positive $z$. This same angular coordinate occurs in spherical coordinates. It is defined modulo $2\pi$ away from the polar axis and is nonunique on the axis.