   Chapter 10.4, Problem 37E

Chapter
Section
Textbook Problem

# Find all points of intersection of the given curves.37. r = sinθ, r = 1 − sinθ

To determine

To Find: The points of intersection of the given curve.

Explanation

Given:

The given polar equations are as below.

r=sinθ (1)

r=1sinθ (2)

Calculation:

Calculate the value of r using the equation (1).

r=sinθ

Substitute 0 for θ in the equation (1).

r=sin(0)=0

Calculate the value of x.

x=rcosθ

Substitute 0 for r and 0 for θ .

x=0×cos(0×π180)=0

Calculate the value of y.

y=rsinθ

Substitute 0 for r and 0 for θ .

y=0×sin(0×π180)=0

Similarly calculate the values of x and y using the value of θ from 0 to 360 .

Tabulate the values of x and y in table (1).

 θ r=sinθ x=rcosθ y=rsinθ 0.00 0.00 0.00 0.00 10.00 0.17 0.17 0.03 20.00 0.34 0.32 0.12 30.00 0.50 0.43 0.25 40.00 0.64 0.49 0.41 50.00 0.77 0.49 0.59 60.00 0.87 0.43 0.75 70.00 0.94 0.32 0.88 80.00 0.98 0.17 0.97 90.00 1.00 0.00 1.00 100.00 0.98 -0.17 0.97 110.00 0.94 -0.32 0.88 120.00 0.87 -0.43 0.75 130.00 0.77 -0.49 0.59 140.00 0.64 -0.49 0.41 150.00 0.50 -0.43 0.25 160.00 0.34 -0.32 0.12 170.00 0.17 -0.17 0.03 180.00 0.00 0.00 0.00 190.00 -0.17 0.17 0.03 200.00 -0.34 0.32 0.12 210.00 -0.50 0.43 0.25 220.00 -0.64 0.49 0.41 230.00 -0.77 0.49 0.59 240.00 -0.87 0.43 0.75 250.00 -0.94 0.32 0.88 260.00 -0.98 0.17 0.97 270.00 -1.00 0.00 1.00 280.00 -0.98 -0.17 0.97 290.00 -0.94 -0.32 0.88 300.00 -0.87 -0.43 0.75 310.00 -0.77 -0.49 0.59 320.00 -0.64 -0.49 0.41 330.00 -0.50 -0.43 0.25 340.00 -0.34 -0.32 0.12 350.00 -0.17 -0.17 0.03 360.00 0.00 0.00 0.00

Calculate the value of r using the equation (2).

r=1sinθ

Substitute 0 for θ in the equation (2).

r=1sin(0)=1

Calculate the value of x.

x=rcosθ

Substitute 1 for r and 0 for θ .

x=1×cos(0×π180)=1

Calculate the value of y.

y=rsinθ

Substitute 1 for r and 0 for θ

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