Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2024 / Paper 2 / 2

The radial coordinate in the cylindrical coordinate system is the Euclidean distance from the $z$-axis:

In spherical coordinates, the radial distance is $\sqrt{x^2+y^2+z^2}=\sqrt{3}$ and $\cos \theta =z/r$. Since the point lies below the equatorial plane, the polar angle exceeds $\pi /2$:The angle is approximately $2.1863$ radians, or $125.26^{\circ }$.