   Chapter 10.4, Problem 24E

Chapter
Section
Textbook Problem

# Find the area of the region that lies inside the first curve and outside the second curve.24. r = 1 − sin θ, r = 1

To determine

To find: The area of the region that lies inside the first curve and outside the second curve.

Explanation

Given:

The polar equation is as below.

r=1sinθ (1)

r=1 (2)

Calculation:

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

r=1sinθ

Substitute 0 for θ in the equation (1).

r=1sin(0×π180)=1

Calculate the value of x.

x=rcosθ

Substitute 1 for r and 0 for θ .

x=rcosθ=1×cos(0×π180)=1

Calculate the value of y.

y=rsinθ

Substitute 1 for r and 0 for θ .

y=1×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=1−sinθ x=rcosθ y=rsinθ 0.00 1.00 1.00 0.00 10.00 0.83 0.81 0.14 20.00 0.66 0.62 0.23 30.00 0.50 0.43 0.25 40.00 0.36 0.27 0.23 50.00 0.23 0.15 0.18 60.00 0.13 0.07 0.12 70.00 0.06 0.02 0.06 80.00 0.02 0.00 0.01 90.00 0.00 0.00 0.00 100.00 0.02 0.00 0.01 110.00 0.06 -0.02 0.06 120.00 0.13 -0.07 0.12 130.00 0.23 -0.15 0.18 140.00 0.36 -0.27 0.23 150.00 0.50 -0.43 0.25 160.00 0.66 -0.62 0.23 170.00 0.83 -0.81 0.14 180.00 1.00 -1.00 0.00 190.00 1.17 -1.16 -0.20 200.00 1.34 -1.26 -0.46 210.00 1.50 -1.30 -0.75 220.00 1.64 -1.26 -1.06 230.00 1.77 -1.14 -1.35 240.00 1.87 -0.93 -1.62 250.00 1.94 -0.66 -1.82 260.00 1.98 -0.34 -1.95 270.00 2.00 0.00 -2.00 280.00 1.98 0.34 -1.95 290.00 1.94 0.66 -1.82 300.00 1.87 0.93 -1.62 310.00 1.77 1.14 -1.35 320.00 1.64 1.26 -1.06 330.00 1.50 1.30 -0.75 340.00 1.34 1.26 -0.46 350.00 1.17 1.16 -0.20 360.00 1.00 1.00 0.00

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

x=rcosθ

Substitute 1 for r and 0 for θ .

x=rcosθ=1×cos(0×π180)=1

Calculate the value of y.

y=rsinθ

Substitute 1 for r and 0 for θ .

y=1×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 (2).

 θ Radius(r) x=rcosθ y=rsinθ 0.00 1 1.00 0.00 10.00 1 0.98 0.17 20.00 1 0.94 0.34 30.00 1 0.87 0.50 40.00 1 0.77 0.64 50.00 1 0.64 0.77 60.00 1 0.50 0.87 70.00 1 0.34 0.94 80.00 1 0.17 0.98 90.00 1 0.00 1.00 100.00 1 -0.17 0.98 110.00 1 -0.34 0.94 120

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### 22. Write as a difference involving two binomials.

Mathematical Applications for the Management, Life, and Social Sciences

#### Evaluate the integral. 12. 0/2(2sin)2d

Single Variable Calculus: Early Transcendentals

#### For f(x) = ex x, f(x) = a) ex x b) ex 1 c) e1 x d) e1 1

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

#### The angle θ at the right has cosine:

Study Guide for Stewart's Multivariable Calculus, 8th 