   Chapter 10.4, Problem 41E

Chapter
Section
Textbook Problem

# Find all points of intersection of the given curves.41. r = sinθ, r = sin 2θ

To determine

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

Explanation

Given:

The given polar equations are given as below.

r=sinθ (1)

r=sin2θ (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=sin2θ

Substitute 0 for θ in the equation (2).

r=sin2(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 (2).

 θ r=sin2θ x=rcosθ y=rsinθ 0

### 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

#### Find the general indefinite integral. (1+rr)2dr

Single Variable Calculus: Early Transcendentals

#### Verify directly that n(AB)=n(A)+n(B)n(AB) for the sets in Exercise 3.

Finite Mathematics for the Managerial, Life, and Social Sciences

#### Using for |x| < 1 and differentiation, find a power series for .

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

#### For what values of p does the series converge?

Study Guide for Stewart's Multivariable Calculus, 8th 