BuyFindarrow_forward

Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643
BuyFindarrow_forward

Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643
Textbook Problem

Find the points on the curve where the tangent is horizontal or vertical. If you have a graphing device, graph the curve to check your work.

19. x = cos θ, y = cos 3θ

To determine

To find: The equation for horizontal or vertical tangent is horizontal lines and plot the curve for the parametric equations x=cosθ and y=cos3θ .

Explanation

Given:

The parametric equation for the variable x is as follows.

x=cosθ (1)

The parametric equation for the variable y is as follows.

y=cos3θ (2)

Calculation:

Differentiate the parametric equation for x with respect to θ .

x=cosθdxdθ=sinθ

Differentiate the parametric equation for y with respect to θ .

y=cos3θdydt=3sin3θ

The tangent is horizontal when the expression dydt=0 is true.

dydt=03sin3θ=03θ=πθ=0,π,π3,2π3 (sinx=0x=nπ)

Substitute (0) for θ in equation (1).

x=cosθ=cos(0)=1

Substitute (0) for θ in equation (2).

y=cos3θ=cos3(0)=1

Substitute (π) for θ in equation (1).

x=cosθ=cos(π)=1

Substitute (π) for θ in equation (2).

y=cos3θ=cos3(π)=1

Substitute (π3) for θ in equation (1).

x=cosθ=cos(π3)=12

Substitute (π3) for θ in equation (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

Chapter 10 Solutions

Show all chapter solutions add
Sect-10.1 P-11ESect-10.1 P-12ESect-10.1 P-13ESect-10.1 P-14ESect-10.1 P-15ESect-10.1 P-16ESect-10.1 P-17ESect-10.1 P-18ESect-10.1 P-19ESect-10.1 P-20ESect-10.1 P-21ESect-10.1 P-22ESect-10.1 P-23ESect-10.1 P-24ESect-10.1 P-25ESect-10.1 P-26ESect-10.1 P-27ESect-10.1 P-28ESect-10.1 P-29ESect-10.1 P-30ESect-10.1 P-31ESect-10.1 P-32ESect-10.1 P-33ESect-10.1 P-34ESect-10.1 P-35ESect-10.1 P-36ESect-10.1 P-37ESect-10.1 P-38ESect-10.1 P-39ESect-10.1 P-40ESect-10.1 P-41ESect-10.1 P-42ESect-10.1 P-43ESect-10.1 P-44ESect-10.1 P-45ESect-10.1 P-46ESect-10.1 P-47ESect-10.1 P-48ESect-10.1 P-49ESect-10.1 P-50ESect-10.1 P-51ESect-10.1 P-52ESect-10.2 P-1ESect-10.2 P-2ESect-10.2 P-3ESect-10.2 P-4ESect-10.2 P-5ESect-10.2 P-6ESect-10.2 P-7ESect-10.2 P-8ESect-10.2 P-9ESect-10.2 P-10ESect-10.2 P-11ESect-10.2 P-12ESect-10.2 P-13ESect-10.2 P-14ESect-10.2 P-15ESect-10.2 P-16ESect-10.2 P-17ESect-10.2 P-18ESect-10.2 P-19ESect-10.2 P-20ESect-10.2 P-21ESect-10.2 P-22ESect-10.2 P-23ESect-10.2 P-24ESect-10.2 P-25ESect-10.2 P-26ESect-10.2 P-27ESect-10.2 P-28ESect-10.2 P-29ESect-10.2 P-30ESect-10.2 P-31ESect-10.2 P-32ESect-10.2 P-33ESect-10.2 P-34ESect-10.2 P-35ESect-10.2 P-36ESect-10.2 P-37ESect-10.2 P-38ESect-10.2 P-39ESect-10.2 P-40ESect-10.2 P-41ESect-10.2 P-42ESect-10.2 P-43ESect-10.2 P-44ESect-10.2 P-45ESect-10.2 P-46ESect-10.2 P-47ESect-10.2 P-48ESect-10.2 P-49ESect-10.2 P-50ESect-10.2 P-51ESect-10.2 P-52ESect-10.2 P-53ESect-10.2 P-54ESect-10.2 P-55ESect-10.2 P-57ESect-10.2 P-58ESect-10.2 P-59ESect-10.2 P-60ESect-10.2 P-61ESect-10.2 P-62ESect-10.2 P-63ESect-10.2 P-64ESect-10.2 P-65ESect-10.2 P-66ESect-10.2 P-67ESect-10.2 P-68ESect-10.2 P-69ESect-10.2 P-70ESect-10.2 P-71ESect-10.2 P-72ESect-10.2 P-73ESect-10.2 P-74ESect-10.3 P-1ESect-10.3 P-2ESect-10.3 P-3ESect-10.3 P-4ESect-10.3 P-5ESect-10.3 P-6ESect-10.3 P-7ESect-10.3 P-8ESect-10.3 P-9ESect-10.3 P-10ESect-10.3 P-11ESect-10.3 P-12ESect-10.3 P-13ESect-10.3 P-14ESect-10.3 P-15ESect-10.3 P-16ESect-10.3 P-17ESect-10.3 P-18ESect-10.3 P-19ESect-10.3 P-20ESect-10.3 P-21ESect-10.3 P-22ESect-10.3 P-23ESect-10.3 P-24ESect-10.3 P-25ESect-10.3 P-26ESect-10.3 P-27ESect-10.3 P-28ESect-10.3 P-29ESect-10.3 P-30ESect-10.3 P-31ESect-10.3 P-32ESect-10.3 P-33ESect-10.3 P-34ESect-10.3 P-35ESect-10.3 P-36ESect-10.3 P-37ESect-10.3 P-38ESect-10.3 P-39ESect-10.3 P-40ESect-10.3 P-41ESect-10.3 P-42ESect-10.3 P-43ESect-10.3 P-44ESect-10.3 P-45ESect-10.3 P-46ESect-10.3 P-47ESect-10.3 P-48ESect-10.3 P-49ESect-10.3 P-50ESect-10.3 P-51ESect-10.3 P-52ESect-10.3 P-53ESect-10.3 P-54ESect-10.3 P-55ESect-10.3 P-56ESect-10.3 P-57ESect-10.3 P-58ESect-10.3 P-59ESect-10.3 P-60ESect-10.3 P-61ESect-10.3 P-62ESect-10.3 P-63ESect-10.3 P-64ESect-10.3 P-65ESect-10.3 P-66ESect-10.3 P-67ESect-10.3 P-68ESect-10.3 P-69ESect-10.3 P-70ESect-10.3 P-71ESect-10.3 P-72ESect-10.3 P-73ESect-10.3 P-74ESect-10.3 P-75ESect-10.3 P-76ESect-10.3 P-77ESect-10.3 P-78ESect-10.4 P-1ESect-10.4 P-2ESect-10.4 P-3ESect-10.4 P-4ESect-10.4 P-5ESect-10.4 P-6ESect-10.4 P-7ESect-10.4 P-8ESect-10.4 P-9ESect-10.4 P-10ESect-10.4 P-11ESect-10.4 P-12ESect-10.4 P-13ESect-10.4 P-14ESect-10.4 P-15ESect-10.4 P-16ESect-10.4 P-17ESect-10.4 P-18ESect-10.4 P-19ESect-10.4 P-20ESect-10.4 P-21ESect-10.4 P-22ESect-10.4 P-23ESect-10.4 P-24ESect-10.4 P-25ESect-10.4 P-26ESect-10.4 P-27ESect-10.4 P-28ESect-10.4 P-29ESect-10.4 P-30ESect-10.4 P-31ESect-10.4 P-32ESect-10.4 P-33ESect-10.4 P-34ESect-10.4 P-35ESect-10.4 P-36ESect-10.4 P-37ESect-10.4 P-38ESect-10.4 P-39ESect-10.4 P-40ESect-10.4 P-41ESect-10.4 P-42ESect-10.4 P-43ESect-10.4 P-44ESect-10.4 P-45ESect-10.4 P-46ESect-10.4 P-47ESect-10.4 P-48ESect-10.4 P-49ESect-10.4 P-50ESect-10.4 P-51ESect-10.4 P-52ESect-10.4 P-53ESect-10.4 P-54ESect-10.4 P-55ESect-10.4 P-56ESect-10.5 P-1ESect-10.5 P-2ESect-10.5 P-3ESect-10.5 P-4ESect-10.5 P-5ESect-10.5 P-6ESect-10.5 P-7ESect-10.5 P-8ESect-10.5 P-9ESect-10.5 P-10ESect-10.5 P-11ESect-10.5 P-12ESect-10.5 P-13ESect-10.5 P-14ESect-10.5 P-15ESect-10.5 P-16ESect-10.5 P-17ESect-10.5 P-18ESect-10.5 P-19ESect-10.5 P-20ESect-10.5 P-21ESect-10.5 P-22ESect-10.5 P-23ESect-10.5 P-24ESect-10.5 P-25ESect-10.5 P-26ESect-10.5 P-27ESect-10.5 P-28ESect-10.5 P-29ESect-10.5 P-30ESect-10.5 P-31ESect-10.5 P-32ESect-10.5 P-33ESect-10.5 P-34ESect-10.5 P-35ESect-10.5 P-36ESect-10.5 P-37ESect-10.5 P-38ESect-10.5 P-39ESect-10.5 P-40ESect-10.5 P-41ESect-10.5 P-42ESect-10.5 P-43ESect-10.5 P-44ESect-10.5 P-45ESect-10.5 P-46ESect-10.5 P-47ESect-10.5 P-48ESect-10.5 P-49ESect-10.5 P-50ESect-10.5 P-51ESect-10.5 P-52ESect-10.5 P-53ESect-10.5 P-54ESect-10.5 P-55ESect-10.5 P-56ESect-10.5 P-57ESect-10.5 P-58ESect-10.5 P-59ESect-10.5 P-60ESect-10.5 P-61ESect-10.5 P-62ESect-10.5 P-63ESect-10.5 P-64ESect-10.5 P-65ESect-10.5 P-66ESect-10.6 P-1ESect-10.6 P-2ESect-10.6 P-3ESect-10.6 P-4ESect-10.6 P-5ESect-10.6 P-6ESect-10.6 P-7ESect-10.6 P-8ESect-10.6 P-9ESect-10.6 P-10ESect-10.6 P-11ESect-10.6 P-12ESect-10.6 P-13ESect-10.6 P-14ESect-10.6 P-15ESect-10.6 P-16ESect-10.6 P-17ESect-10.6 P-18ESect-10.6 P-19ESect-10.6 P-20ESect-10.6 P-21ESect-10.6 P-22ESect-10.6 P-23ESect-10.6 P-24ESect-10.6 P-25ESect-10.6 P-26ESect-10.6 P-27ESect-10.6 P-28ESect-10.6 P-29ESect-10.6 P-30ESect-10.6 P-31ECh-10 P-1RCCCh-10 P-2RCCCh-10 P-3RCCCh-10 P-4RCCCh-10 P-5RCCCh-10 P-6RCCCh-10 P-7RCCCh-10 P-8RCCCh-10 P-9RCCCh-10 P-1RQCh-10 P-2RQCh-10 P-3RQCh-10 P-4RQCh-10 P-5RQCh-10 P-6RQCh-10 P-7RQCh-10 P-8RQCh-10 P-9RQCh-10 P-10RQCh-10 P-1RECh-10 P-2RECh-10 P-3RECh-10 P-4RECh-10 P-5RECh-10 P-6RECh-10 P-7RECh-10 P-8RECh-10 P-9RECh-10 P-10RECh-10 P-11RECh-10 P-12RECh-10 P-13RECh-10 P-14RECh-10 P-15RECh-10 P-16RECh-10 P-17RECh-10 P-18RECh-10 P-19RECh-10 P-20RECh-10 P-21RECh-10 P-22RECh-10 P-23RECh-10 P-24RECh-10 P-25RECh-10 P-26RECh-10 P-27RECh-10 P-28RECh-10 P-29RECh-10 P-30RECh-10 P-31RECh-10 P-32RECh-10 P-33RECh-10 P-34RECh-10 P-35RECh-10 P-36RECh-10 P-37RECh-10 P-38RECh-10 P-39RECh-10 P-40RECh-10 P-41RECh-10 P-42RECh-10 P-43RECh-10 P-44RECh-10 P-45RECh-10 P-46RECh-10 P-47RECh-10 P-48RECh-10 P-49RECh-10 P-50RECh-10 P-51RECh-10 P-52RECh-10 P-53RECh-10 P-54RECh-10 P-55RECh-10 P-56RECh-10 P-57RECh-10 P-58RECh-10 P-1PCh-10 P-2PCh-10 P-3PCh-10 P-4PCh-10 P-5PCh-10 P-6P

Additional Math Solutions

Find more solutions based on key concepts

Show solutions add

Evaluate the expression sin Exercises 116. (23)2

Finite Mathematics and Applied Calculus (MindTap Course List)

Use the properties of integrals to verify the inequality. 01excosxdxe1

Single Variable Calculus: Early Transcendentals, Volume I

Quotients Evaluate the quotient, and write the result in the form a + bi. 38. 11+i

Precalculus: Mathematics for Calculus (Standalone Book)

In Exercises 3540, rationalize the numerator of each expression. 39. 1+x+2x+2

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

Add: 832+9+56+2358

Elementary Technical Mathematics

If the drawing, HJKFGK. If HK=6,KF=8, and FG=5, find HJ.

Elementary Geometry For College Students, 7e

Round the following numbers to the indicated place. 13. 4.6935 to tenths

Contemporary Mathematics for Business & Consumers

For the probability density function in question 2, the probability of observing a value of greater than 2 is: ...

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

What is the primary advantage of self-report measures? What is the primary disadvantage?

Research Methods for the Behavioral Sciences (MindTap Course List)