Cylindrical coordinates to cartesian coordinates

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

I've tried this way:

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

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