\begin{align} r&=\sqrt{\rho^2 + z^2} \\ \theta&=\arctan\frac{\rho}{z}=\arccos\frac{z}{\sqrt{\rho^2 + z^2}} \\ \varphi&=\varphi \end{align} .
\begin{align} \rho &= r \sin \theta \\ \varphi &= \varphi \\ z &= r \cos \theta \end{align} .