Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2010 / Paper 2 / 11 / a

In plane polar coordinates, $r$ is distance from the origin and $\theta$ is the angle from positive $x$ toward positive $y$. The conversion to Cartesian coordinates isConversely $r=\sqrt{x^2+y^2}$, with the angular coordinate undefined at the origin.