   Chapter 11.7, Problem 66E

Chapter
Section
Textbook Problem

# Cylindrical-to-Spherical Conversion In Exercises 63-70, convert the point from cylindrical coordinates to spherical coordinates. ( 2 , 2 π 3 , − 2 )

To determine

To calculate: The spherical coordinates from the cylindrical coordinates (2,2π3,2).

Explanation

Given:

The cylindrical coordinate is:

(2,2π3,2)

Formula used:

For the conversion of cylindrical coordinate into spherical coordinate following substitutiontakes place:

ρ=r2+z2θ=θφ=arccoszr2+z2

Calculation:

For cylindrical coordinates (2,2π3,2)=(r,θ,z)

Therefore,

r=2,θ=2π3,z=2

Since, ρ=r2+z2

Substitute the values from the above relations,

ρ=(2)2+(2)2=

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