   Chapter 15.8, Problem 4E

Chapter
Section
Textbook Problem

Change from rectangular to spherical coordinates.4. (a) (1, 0, 3 ) (b) ( 3 , –1, 2 3 )

(a)

To determine

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

Explanation

Given:

The rectangular coordinates (1,0,3) .

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=1,y=0,z=3 . Therefore, by the formula mentioned above, the spherical coordinates are obtained as follows.

The ρ - value is,

ρ=(1)2+(0)2+(3)2=1<

(b)

To determine

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

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