# Polar coordinates

Polar coordinates in the $xy$-plane are given by the variable assignments $$\left\{ \begin{array}{ll} x &= r\cos(\theta) \\ y &= r\sin(\theta) \end{array} \right.,$$ and coincidentally, the Pythagorean identity for sin and cos implies that $r=\sqrt{x^2+y^2}$ and that $\theta=\mathrm{arctan} \left( \dfrac{y}{x} \right)$ follows from the definition of tangent and application of the inverse tangent function.