Question

To convert from spherical to rectangular coordinates:

$x=-----,y=-----,z=-----$

Short answer

$x=\rho \sin \varphi \cos \theta ,y=\rho \sin \varphi \sin \theta ,z=\rho \cos \varphi$

Step-by-step solution

Given Information

Given$\left(x,y,z\right)$are rectangular coordinates and$\left(\rho ,\theta ,\varphi \right)$are spherical coordinates.

Simplification

$\left(x,y,z\right)$are rectangular coordinates and localid="1651603565768" $\left(\rho ,\theta ,\varphi \right)$are spherical coordinates.

The relation is as below:

localid="1653232572011" role="math" $x=\rho \sin \varphi \cos \theta ,y=\rho \sin \varphi \sin \theta ,z=\rho \cos \varphi$

Hence,
$x=\rho \sin \varphi \cos \theta$

$y=\rho \sin \varphi \sin \theta$

and$z=\rho \cos \varphi$