   Chapter 15.8, Problem 3E

Chapter
Section
Textbook Problem

Change from rectangular to spherical coordinates.3.(a) (0, –2, 0) (b) (–1, 1, – 2 )

(a)

To determine

To change: The given point into the corresponding spherical coordinates.

Explanation

Given:

The rectangular coordinates (0,2,0) .

Formula used:

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

ρ=x2+y2+z2ϕ=cos1(zρ)θ=cos1(xρsinϕ)

Calculation:

From the given conditions, it is observed that x=0,y=2,z=0 . Therefore, by the formula mentioned above, the spherical coordinates are obtained as follows.

The ρ - value is,

ρ=(0)2+(2)2+(0)2=0+4+0=4

(b)

To determine

To change: The given point into the corresponding spherical coordinates.

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