   Chapter 10.5, Problem 52E

Chapter
Section
Textbook Problem

Area Sketch the strophoid r = sec θ − 2 cos θ ,   − π 2 < θ < π 2 . Convert this equation to rectangular coordinates. Find the area enclosed by the loop.

To determine

To graph: The strophoid r=secθ2cosθ, π2<θ<π2 and convert this equation into rectangular coordinates and also to find the area by the enclosed loop.

Explanation

Given:

Polar equation is given r=secθ2cosθ and the interval is given π2<θ<π2

Graph:

Use graphing calculator to sketch graph and area is symmetric about x- axis so the area can be calculated using integration as

A=20π412r2.dθ

Consider, r=secθ2cosθ

Graph of curve is shown below:

Now, convert the equation into rectangular coordinates,

Consider, r=secθ2cosθ

r=1cosθ2cosθrcosθ=12cos2θrcosθ=12(xr)2

Multiply r2 both sides and get,

r3cosθ=r22r2(xr)2r2(rcosθ)=r22x2(x2+y2)x=x2+y22x2x3+y2x=y2x2

That is

x2(1+x)=y2(1x)

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

Expand each expression in Exercises 122. (2xy)y

Finite Mathematics and Applied Calculus (MindTap Course List)

In Exercises 39-54, simplify the expression. (Assume that x, y, r, s, and t are positive.) 41. (x2y3) (x5y3)

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

In problems 1-16, solve each equation. 15. Solve

Mathematical Applications for the Management, Life, and Social Sciences

Find the unit tangent vector for at t = –1.

Study Guide for Stewart's Multivariable Calculus, 8th

ex(ex)2 = a) ex3 b) e3x c) 3ex d) e4x

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