# How to convert cylindrical coordinate to cartesian coordinate?

1. Oct 27, 2008

### kloong

1. The problem statement, all variables and given/known data
Cylindrical: (5,5,53.2)
Cartesian = ??

How bout Cartesian to coordinate?
Any websites that shows all the conversions?

2. Oct 27, 2008

### HallsofIvy

Staff Emeritus
Cylindrical coordinates is just polar coordinates in the xy-plane together with the z coordinate. Do you know $x= r cos(\theta)$ and $y= r sin(\theta)$.
Then $x^2+ y^2= r^2 cos^2(\theta)+ r^2 sin^2\(theta)= r^2$. Also, dividing one equation by the other, $y/x= (r sin(\theta))/(r cos(\theta))= tan(\theta)$. Putting that all together,

$$r= \sqrt{x^2+ y^2}$$
$$\theta= tan^{-1}(\frac{y}{x})$$
z= z