   Chapter 10.3, Problem 31E

Chapter
Section
Textbook Problem

Sketch the curve with the given polar equation by first sketching the graph of r as a function of θ in Cartesian coordinates.31. r = 2(1 + cos θ)

To determine

To sketch: The curves for the polar equation r=2(1+cosθ) and its Cartesian coordinates.

Explanation

Given:

The polar equation is r=2(1+cosθ) .

Calculation:

Substitute (0) for θ in equation r=2(1+cosθ) ,

r=2(1+cosθ)=2(1+cos(0))=4

For the polar equation r=2(1+cosθ) values for the Cartesian coordinates curve is tabulated below.

 θ r 0 4 0.174611111 3.9695883 0.349222222 3.8792783 0.523833333 3.7318162 0.698444444 3.5316868

Graph:

The curve for the Cartesian coordinates is shown below in figure 1

From the figure 1, when θ increases from 0 to π2 , the polar curve r decreases from 4 to 2 in polar graph

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