Cylindrical Coordinates

Extension of polar coordinates into 3D. Really simple - just add $z$. The $r$ and $\theta$ are the same as polar coordinates.

Conversion from cylindrical to Cartesian:

$$\begin{array}{rl}x& =r\cos \theta \\ y& =r\sin \theta \\ z& =z\end{array}$$

Conversion from Cartesian to cylindrical:

$$\begin{array}{rl}r& =\sqrt{x^2+y^2}\\ \theta & ={\tan }^{-1}\left(\frac{y}{x}\right)\\ z& =z\end{array}$$