#todo > [!NOTE] Definition (Cylindrical Coordinates) > Let $(x,y,z)\in \mathbb{R}^{3}$ be an element of the [[Real n-Space|real 3-space]]. Then its **cylindrical coordinates** are given by $(r,\theta, z)$ where $x=r\cos\theta,\quad y = r\sin \theta, \quad z=z$and $r,\phi,z$ are called the **radial**, **azimuthal**, and **vertical coordinates** respectively. # Properties In short: cylindrical coordinates = polar + z. ???