Solution (source code)

= Solution

Project the radius <vector> onto the $x$-$y$ <plane>. The <polar angle> $\theta=\pi/6$ lies between the positive $z$ axis and $OP$. The <azimuth> $\phi=\pi/3$ lies in the $x$-$y$ <plane> between the positive $x$ axis and the projection of $OP$, measured toward positive $y$.

\Image[/past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2013/paper-2-spherical-angles.png]
{title=Polar and azimuthal angles of the specified point in spherical coordinates}