Polar Coordinate System

Polar Coordinates

Polar coordinates uniquely identify each point in the Euclidean space ${\mathbb{R}}^2$ by its distance $r$ from the origin and the angle $\theta$ it makes with the $x$-axis.

Conventions

Technically, each point has infinitely many polar coordinates, since adding or substracting a multiple of $2\pi$ to an angle has no effect. However, in order to have a coordinate system, coordinates must be unique which means that the range of values for $\theta$ needs to be restricted. The most common conventions for the possible values of $\theta$ are $[0;2\pi )$ and $(-\pi ;\pi ]$.