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How to convert cylindrical coordinate to cartesian coordinate?

  1. Oct 27, 2008 #1
    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. jcsd
  3. Oct 27, 2008 #2

    HallsofIvy

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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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