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Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550

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BuyFindarrow_forward

Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550
Textbook Problem

The rectangular coordinates of a point are (2, 2, −1). Find the cylindrical and spherical coordinates of the point.

To determine

To find: The corresponding cylindrical and spherical coordinates for the given rectangular coordinates.

Explanation

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+z2ϕ=cos1(zρ)θ=cos1(xρsinϕ) (2)

Given:

The rectangular coordinates (2,2,1) .

Calculation:

From the given conditions, it is observed that x=2,y=2,z=1 .

Obtain the cylindrical coordinates by the formula (1) mentioned above.

r=(2)2+(2)2=4+4=8=22

θ=tan1(22)

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Chapter 15 Solutions

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