   Chapter 10, Problem 29RE

Chapter
Section
Textbook Problem

# At what points does the curve x = 2 a cos t − a cos 2 t y = 2 a sin t − a sin 2 t have vertical or horizontal tangents? Use this information to help sketch the curve.

To determine

To find: The point at which the curve has vertical and horizontal tangents and also plots the curve.

Explanation

Given:

The curve equations are as below.

x=2acostacos2t (1)

y=2asintasin2t (2)

Calculation:

Differentiate the equation (1) with respect to t .

x=2acostacos2tdxdt=2asint+2asin2t

Assume dxdt is equal to zero.

dxdt=2asint+2asin2t0=2asint+2asin2t2asint+4asintcost=02asint(2cost1)=0

Calculate the value of sint and cost from the above equation.

2asint(2cost1)=02cost1=0cost=12

Take the values of t to get cost=12 . Therefore, the value of t is to be taken as π3 or 5π3 .

Then, apply the condition as below.

2asint(2cost1)=02asint=0sint=0

Take the values of t to get sint=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

#### Expand each expression in Exercises 122. (x2+x1)(2x+4)

Finite Mathematics and Applied Calculus (MindTap Course List)

#### In Exercises 107-120, factor each expression completely. 111. 10 14x 12x2

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

#### Identify and describe the steps of the scientific method.

Research Methods for the Behavioral Sciences (MindTap Course List) 