Q 12. - Calculus

Question

To convert from spherical to cylindrical coordinates:

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

Step-by-Step Solution

Answer

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

Step 1: Given Information

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

Step 2: Simplification

The relation between two is:

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

Hence,

$r=\rho \sin \varphi$

$\theta =\theta$

and

$z=\rho \cos \varphi$