Chapter 15, Problem 11RE

### Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550

Chapter
Section

### Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550
Textbook Problem

# The cylindrical coordinates of a point are ( 2 3 , π 3 , 2). Find the rectangular and spherical coordinates of the point.

To determine

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

Explanation

Formula used:

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

x=rcosθy=rsinθz=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 cylindrical coordinates (23,π3,2) .

Calculation:

From the given conditions, it is observed that r=23,θ=π3,z=2 . Therefore by the formula (1) mentioned above,

x=rcosθ=23cos(π3)=23(12)=3

y=23sin(π3)=2332=3

z=z=2

The rectangular coordinates is given by, (3,3,2)

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