Cylindrical coordinates to cartesian coordinates

Telemachus

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!

Raskolnikov

The equation for the plane is just [tex] y = \sqrt{3}x. [/tex]

Telemachus

Thanks Raskolnikov, I didn't see it that way, [tex]y = \sqrt{3}x\forall{z}[/tex]