cylindrical coordinates

Cylindrical coordinates are a system of coordinates for ${ℝ}^3$. Two of the coordinates correspond to the polar coordinates of ${ℝ}^2$, and the third coordinate corresponds with the $z$ axis. Thus, the coordinates are given by

$$\left(\begin{array}{c}\hfill x\hfill \\ \hfill y\hfill \\ \hfill z\hfill \end{array}\right)=\left(\begin{array}{c}\hfill r\cos \theta \hfill \\ \hfill r\sin \theta \hfill \\ \hfill z\hfill \end{array}\right),$$

where $r$ is the distance from $(0,0,0)$ to $(x,y,0)$ and $\theta$ is the azimuthal angle defined for $\theta \in [0,2\pi )$.

Just as with polar coordinates, one can convert from Cartesian coordinates to cylindrical coordinates for any point not lying on the $z$ axis via

$r(x,y)$$=$$\sqrt{x^2+y^2},$

$\theta (x,y)$$=$$\arctan (x,y),$

where $\arctan$ is defined here (http://planetmath.org/OperatornamearcTanWithTwoArguments).