Cylindrical coordinates to cartesian coordinates

[Telemachus]

Homework Statement

Hi there. Hi have in cylindrical coordinates that $$\theta=\displaystyle\frac{\pi}{3}$$, and I must make the graph, and take it into cartesian coordinates. How should I do?

I've tried this way:

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

I think its a semi-plane parallel to the line: $$2\displaystyle\frac{y}{\sqrt[ ]{3}}-2x=0$$. 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 $$y = \sqrt{3}x.$$

 

[Telemachus]

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