The Polar Coordinate System

The polar coordinate system is an alternate coordinate system where the two variables are $r$ and $\theta$, instead of $x$ and $y$.

Polar and Cartesian coordinates can be interconverted using the Pythagorean Theorem and trigonometry.

Polar coordinates allow conic sections to be expressed in an elegant way.

Some curves have a simple expression in polar coordinates, whereas they would be very complex to represent in Cartesian coordinates.