   Chapter 15, Problem 15RE

Chapter
Section
Textbook Problem

Write the equation in cylindrical coordinates and in spherical coordinates.(a) x2 + y2 + z2 = 4 (b) x2 + y2 = 4

(a)

To determine

To rewrite: The given equation in the cylindrical and spherical coordinates.

Explanation

Given:

The equation in rectangular coordinates is, x2+y2+z2=4 .

Formula used:

The cylindrical coordinates (r,θ,z) corresponding to the rectangular coordinates (x,y,z) is,

r=x2+y2θ=tan1(yx)z=z (1)

The spherical coordinates (ρ,θ,ϕ) corresponding to the rectangular coordinates (x,y,z) is,

ρ=x2+y2+z2</

(b)

To determine

To rewrite: The given equation in the cylindrical and spherical coordinates.

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