   Chapter 10, Problem 13RE

Chapter
Section
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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