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Cylindrical coordinates to cartesian coordinates

  1. Aug 30, 2010 #1
    1. The problem statement, all variables and given/known data
    Hi there. Hi have in cylindrical coordinates that [tex]\theta=\displaystyle\frac{\pi}{3}[/tex], and I must make the graph, and take it into cartesian coordinates. How should I do?

    I've tried this way:

    [tex]\begin{Bmatrix}x=r\cos\displaystyle\frac{\pi}{3}\\y=r\sin\displaystyle\frac{\pi}{3} \\z=z\end{matrix}\Rightarrow{\begin{Bmatrix}x=\displaystyle\frac{r}{2}\\y={r\displaystyle\frac{\sqrt[ ]{3}}{2} \\z=z\end{matrix}}[/tex]

    I think its a semi-plane parallel to the line: [tex]2\displaystyle\frac{y}{\sqrt[ ]{3}}-2x=0[/tex]. I thought of working geometrically with it, taking another point. Or taking three points, but I think its probably easier someway, just from the equations system. I don't know how to take x and y, to make them a function of z.

    Bye there!
  2. jcsd
  3. Aug 30, 2010 #2
    The equation for the plane is just [tex] y = \sqrt{3}x. [/tex]
  4. Aug 30, 2010 #3
    Thanks Raskolnikov, I didn't see it that way, [tex]y = \sqrt{3}x\forall{z}[/tex]
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