Space/Cylindrical coordinates/Angle naive/Example

A spatial variant of the polar coordinates are the so-called cylindrical coordinates. A triple ${}(r,\alpha ,z)\in \mathbb {R} _{+}\times [0,2\pi [\times \mathbb {R}$ is sent to the Cartesian coordinates

${}(x,y,z)=(r\cos \alpha ,r\sin \alpha ,z)\,.$