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).

Title	cylindrical coordinates
Canonical name	CylindricalCoordinates
Date of creation	2013-03-22 17:01:54
Last modified on	2013-03-22 17:01:54
Owner	Wkbj79 (1863)
Last modified by	Wkbj79 (1863)
Numerical id	6
Author	Wkbj79 (1863)
Entry type	Definition
Classification	msc 51M05
Related topic	PolarCoordinates
Related topic	SphericalCoordinates