   Chapter 11, Problem 71RE

Chapter
Section
Textbook Problem

# Spherical-to-Cylindrical Conversion In exercises 71 and 72, convert the point from spherical coordinates to cylindrical coordinates. ( 25 , − π 4 , 3 π 4 )

To determine

To calculate: Thecorresponding cylindricalcoordinates for the point (25,π4,3π4) in the spherical coordinates.

Explanation

Given:

The point in spherical coordinatesis (25,π4,3π4).

Formula used:

The conversion equations to convert a point (ρ,θ,ϕ) in spherical coordinate to cylindricalcoordinate (r,θ,z):

r2=ρ2sin2ϕ , r0 θ=θ z=ρcosϕ

Calculation:

The point inspherical coordinatesis (25,π4,3π4).(81,5π6,273). As, coordinate of any point in spherical coordinate are (ρ,θ,ϕ).

Therefore,

ρ=25θ=π4ϕ=3π4

Now, the conversion equations to convert a point (ρ,θ,ϕ) in spherical coordinate to cylindricalcoordinate (r,θ,z):

r2=ρ2sin2ϕ , r0 θ=θ z=ρcosϕ

Substitute the above values of ρ, θ and z in the above equations to get the coordinates in cylindrical coordinate

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