   Chapter 10.4, Problem 29E

Chapter
Section
Textbook Problem

Find the area of the region that lies inside both curves.29. r = 3 sin θ, r = 3 cos θ

To determine

To Find: The area of the region that lies inside both curves.

Explanation

Given:

The polar equations are as below.

r=3sinθ (1)

r=3cosθ (2)

Calculation:

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

r=3sinθ

Substitute 0 for θ in the equation (1).

r=3sin(0×π180)=0

Calculate the value of x.

x=rcosθ

Substitute 0 for r and 0 for θ .

x=rcosθ=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=3sinθ x=rcosθ y=rsinθ 0.00 0.00 0.00 0.00 10.00 0.52 0.51 0.09 20.00 1.03 0.96 0.35 30.00 1.50 1.30 0.75 40.00 1.93 1.48 1.24 50.00 2.30 1.48 1.76 60.00 2.60 1.30 2.25 70.00 2.82 0.96 2.65 80.00 2.95 0.51 2.91 90.00 3.00 0.00 3.00 100.00 2.95 -0.51 2.91 110.00 2.82 -0.96 2.65 120.00 2.60 -1.30 2.25 130.00 2.30 -1.48 1.76 140.00 1.93 -1.48 1.24 150.00 1.50 -1.30 0.75 160.00 1.03 -0.96 0.35 170.00 0.52 -0.51 0.09 180.00 0.00 0.00 0.00 190.00 -0.52 0.51 0.09 200.00 -1.03 0.96 0.35 210.00 -1.50 1.30 0.75 220.00 -1.93 1.48 1.24 230.00 -2.30 1.48 1.76 240.00 -2.60 1.30 2.25 250.00 -2.82 0.96 2.65 260.00 -2.95 0.51 2.91 270.00 -3.00 0.00 3.00 280.00 -2.95 -0.51 2.91 290.00 -2.82 -0.96 2.65 300.00 -2.60 -1.30 2.25 310.00 -2.30 -1.48 1.76 320.00 -1.93 -1.48 1.24 330.00 -1.50 -1.30 0.75 340.00 -1.03 -0.96 0.35 350.00 -0.52 -0.51 0.09 360.00 0.00 0.00 0.00

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

r=3cosθ

Substitute 0 for θ in the equation (2).

r=3cos(0×π180)=3

Calculate the value of x.

x=rcosθ

Substitute 3 for r and 0 for θ .

x=rcosθ=3×cos(0×π180)=3

Calculate the value of y.

y=rsinθ

Substitute 3 for r and 0 for θ .

y=3×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 r=3cosθ x=rcosθ y=rsinθ 0.00 3.00 3.00 0.00 10.00 2.95 2.91 0.51 20.00 2

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

Write the formula for the declining-balance rate. (17-3)

Contemporary Mathematics for Business & Consumers

True or False: converges absolutely.

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

The curvature of at t = 0 is:

Study Guide for Stewart's Multivariable Calculus, 8th 