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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336

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Section
BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336
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.

32. r = 1 + 2 cos θ

To determine

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

Explanation

Given:

The polar equation is as below.

r=1+2cosθ .

Calculation:

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

r=1+2cosθ=1+2cos(0)=3

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

t r
0 3
0.174611111 2.9695883
0.349222222 2.8792783
0.523833333 2.7318162
0.698444444 2.5316868

Graph:

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

From the figure 1, when θ increases from 0 to 2π3 ., the polar curve r decreases from 3 to 0 in polar graph

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