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How to convert cylindrical coordinate to cartesian coordinate?

  • Thread starter kloong
  • Start date
  • #1
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Homework Statement


Cylindrical: (5,5,53.2)
Cartesian = ??

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

Answers and Replies

  • #2
HallsofIvy
Science Advisor
Homework Helper
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Cylindrical coordinates is just polar coordinates in the xy-plane together with the z coordinate. Do you know [itex]x= r cos(\theta)[/itex] and [itex]y= r sin(\theta)[/itex].
Then [itex]x^2+ y^2= r^2 cos^2(\theta)+ r^2 sin^2\(theta)= r^2[/itex]. Also, dividing one equation by the other, [itex]y/x= (r sin(\theta))/(r cos(\theta))= tan(\theta)[/itex]. Putting that all together,

[tex]r= \sqrt{x^2+ y^2}[/tex]
[tex]\theta= tan^{-1}(\frac{y}{x})[/tex]
z= z
 

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