   Chapter 10, Problem 9RE

Chapter
Section
Textbook Problem

# Sketch the polar curve.9. r = 1 + sin θ

To determine

To find: Sketch the polar curve r=1+sinθ.

Explanation

Given:

The polar equation for the variable r is as follows.

r=1+sinθ (1)

Draw the curve for the values of θ and r.

Determine the value of different values of r.

Substitute the value of 0° for θ.

r=1+(sin0°×π180)=1

Similarly, substitute till 360° for θ.

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

 θ r 0.00 1.00 10.00 1.17 20.00 1.34 30.00 1.50 40.00 1.64 50.00 1.77 60.00 1.87 70.00 1.94 80.00 1.98 90.00 2.00 100.00 1.98 110.00 1.94 120.00 1.87 130.00 1.77 140.00 1.64 150.00 1.50 160.00 1.34 170.00 1.17 180.00 1.00 190.00 0.83 200.00 0.66 210.00 0.50 220.00 0.36 230.00 0.23 240.00 0.13 250.00 0.06 260.00 0.02 270.00 0.00 280.00 0.02 290.00 0.06 300.00 0.13 310.00 0.23 320.00 0.36 330.00 0.50 340.00 0.66 350.00 0.83 360.00 1.00

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=1×cos0°=1

Determine the value of y

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