Question

To convert from spherical to cylindrical coordinates:

$r=----,\theta =----,z=----$

Short answer

$r=\rho \sin \varphi ,\theta =\theta ,z=\rho \cos \varphi$

Step-by-step solution

Given Information

Given $(r,\theta ,z)$be cylindrical coordinates and $(\rho ,\theta ,\varphi )$be spherical coordinates.

Simplification

The relation between two is:

$r=\rho \sin \varphi ,\theta =\theta ,z=\rho \cos \varphi$

Hence,

$r=\rho \sin \varphi$

$\theta =\theta$

and

$z=\rho \cos \varphi$