Chapter 13: Q 10. (page 1066)

To convert from spherical to rectangular coordinates:
$x = - - - - -, y = - - - - -, z = - - - - -$

Short Answer

Expert verified

$x = ρ \sin ϕ \cos θ, y = ρ \sin ϕ \sin θ, z = ρ \cos ϕ$

Step by step solution

Given Information

Given $(x, y, z)$ are rectangular coordinates and $(ρ, θ, ϕ)$ are spherical coordinates.

Simplification

$(x, y, z)$ are rectangular coordinates and localid="1651603565768" $(ρ, θ, ϕ)$ are spherical coordinates.

The relation is as below:

localid="1653232572011" role="math" $x = ρ \sin ϕ \cos θ, y = ρ \sin ϕ \sin θ, z = ρ \cos ϕ$

Hence,
$x = ρ \sin ϕ \cos θ$

$y = ρ \sin ϕ \sin θ$

and $z = ρ \cos ϕ$

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To convert from spherical to rectangular coordinates:
$x = - - - - -, y = - - - - -, z = - - - - -$

Short Answer

Step by step solution

Given Information

Simplification

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To convert from spherical to rectangular coordinates:x=-----,y=-----,z=-----

Short Answer

Step by step solution

Given Information

Simplification

One App. One Place for Learning.

Most popular questions from this chapter

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To convert from spherical to rectangular coordinates:
$x = - - - - -, y = - - - - -, z = - - - - -$