   Chapter 11, Problem 78RE

Chapter
Section
Textbook Problem

# Spherical-to-Rectangular Conversation In exercise 77 and 78, find an equation in rectangular coordinates for the equation given in spherical coordinates, and sketch its graph. ρ = 3 cos ϕ

To determine

To calculate: The corresponding equation in rectangular coordinates for the equation ρ=3cosϕ in spherical coordinates and to sketch its graph.

Explanation

Given:

The equation in spherical coordinates is ρ=3cosϕ.

Formula used:

The conversion equations to convert a point (ρ,θ,ϕ) in spherical coordinate to rectangular coordinate (x,y,z):

x=ρsinϕcosθy=ρsinϕsinθz=ρcosϕ

Calculation:

Consider the equation in spherical coordinate,

ρ=3cosϕ

Multiply both the sides of the equation with ρ to get,

ρ2=3ρcosϕ

Now, as ρcosϕ=z and ρ2=x2+y2+z2

Therefore,

x2+y2+z2=3zx2+y2+z23

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