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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 polar curve.

13. r = 1 + cos 2θ

To determine

To sketch: The polar curve r=1+cos2θ.

Explanation

Given:

The Polar equation for the variable r is as follows.

r=1+cos2θ (1)

Draw the curve for the values of θ and r.

Determine the value of r.

Substitute the value of 0° for θ.

r=(1+(cos(2×0°)×π180))=2

Similarly, substitute till 360° for θ.

Summarize the values of θ and r as shown in the table (1).

θ r
0.00 2.00
10.00 1.94
20.00 1.77
30.00 1.50
40.00 1.17
50.00 0.83
60.00 0.50
70.00 0.23
80.00 0.06
90.00 0.00
100.00 0.06
110.00 0.23
120.00 0.50
130.00 0.83
140.00 1.17
150.00 1.50
160.00 1.77
170.00 1.94
180.00 2.00
190.00 1.94
200.00 1.77
210.00 1.50
220.00 1.17
230.00 0.83
240.00 0.50
250.00 0.23
260.00 0.06
270.00 0.00
280.00 0.06
290.00 0.23
300.00 0.50
310.00 0.83
320.00 1.17
330.00 1.50
340.00 1.77
350.00 1.94
360.00 2.00

Graph:

Draw the polar curve for the values of θ and r as shown in the figure (1) from table 1.

To draw the curve for the values of x and y.

Determine the value of x.

x=rcosθ

Substitute the value of 1 for r and 0° for θ.

x=2×cos0°=2

Determine the value of y

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Chapter 10 Solutions

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Sect-10.1 P-11ESect-10.1 P-12ESect-10.1 P-13ESect-10.1 P-14ESect-10.1 P-15ESect-10.1 P-16ESect-10.1 P-17ESect-10.1 P-18ESect-10.1 P-19ESect-10.1 P-20ESect-10.1 P-21ESect-10.1 P-22ESect-10.1 P-23ESect-10.1 P-24ESect-10.1 P-25ESect-10.1 P-26ESect-10.1 P-27ESect-10.1 P-28ESect-10.1 P-29ESect-10.1 P-30ESect-10.1 P-31ESect-10.1 P-32ESect-10.1 P-33ESect-10.1 P-34ESect-10.1 P-35ESect-10.1 P-36ESect-10.1 P-37ESect-10.1 P-38ESect-10.1 P-39ESect-10.1 P-40ESect-10.1 P-41ESect-10.1 P-42ESect-10.1 P-43ESect-10.1 P-44ESect-10.1 P-45ESect-10.1 P-46ESect-10.1 P-47ESect-10.1 P-48ESect-10.1 P-49ESect-10.1 P-50ESect-10.1 P-51ESect-10.1 P-52ESect-10.2 P-1ESect-10.2 P-2ESect-10.2 P-3ESect-10.2 P-4ESect-10.2 P-5ESect-10.2 P-6ESect-10.2 P-7ESect-10.2 P-8ESect-10.2 P-9ESect-10.2 P-10ESect-10.2 P-11ESect-10.2 P-12ESect-10.2 P-13ESect-10.2 P-14ESect-10.2 P-15ESect-10.2 P-16ESect-10.2 P-17ESect-10.2 P-18ESect-10.2 P-19ESect-10.2 P-20ESect-10.2 P-21ESect-10.2 P-22ESect-10.2 P-23ESect-10.2 P-24ESect-10.2 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P-52RECh-10 P-53RECh-10 P-54RECh-10 P-55RECh-10 P-56RECh-10 P-57RECh-10 P-58RECh-10 P-1PCh-10 P-2PCh-10 P-3PCh-10 P-4PCh-10 P-5PCh-10 P-6P

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