1.2. Polar Coordinates

Polar Coordinates

Polar coordinates represent points in a 2D plane using a distance and an angle rather than Cartesian $(x,y)$. Each point is defined by its radius $r>0$ (distance from origin) and angle $\theta \in [0,2\pi )$ (measured from the positive x-axis), such that
$r=\sqrt{x^2+y^2},\theta ={\tan }^{-1}x/y.$
Conversely, one can go from polar to Cartesian coordinates, such that
$x=r\cos \theta ,y=r\sin \theta .$