Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2013 / Paper 2 / 7 / a

Use the convention that $\theta$ is the polar angle from positive $z$, and $\varphi$ the azimuth from positive $x$. The radius isThen $\cos \theta =z/r=\sqrt{3}/2$, while $\tan \varphi =y/x=\sqrt{3}$ and both planar coordinates are positive. Thus the spherical coordinates are