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