Chapter 10.2, Problem 69E

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

Chapter
Section

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
Textbook Problem

# Think About It The following sets of parametric equations have the same graph. Does this contradict your conjecture from Exercise 68? Explain. x = cos θ ,   y = sin 2 θ ,   0 < θ < π x = cos ( − θ ) ,   y = sin 2 ( − θ ) ,   0 < θ < π

To determine
Does the given sets of parametric equations x=cosθ and

y=sin2θ,0θπ, x=cos(θ) and y=sin2(θ),0θπ contradict the conjecture of

parametric equations having reversed orientation when sign is changed.

Explanation

Given:

The following set of parametric equations:

x=cosÎ¸ and y=sin2Î¸,0â‰¤Î¸â‰¤Ï€

x=cos(âˆ’Î¸) and y=sin2(âˆ’Î¸),0â‰¤Î¸â‰¤Ï€

Explanation:

Consider the given parametric equations.

x=cosÎ¸ and y=sin2Î¸,0â‰¤Î¸â‰¤Ï€ â€¦...â€¦... (1)

x=cos(âˆ’Î¸) and y=sin2(âˆ’Î¸),0â‰¤Î¸â‰¤Ï€ â€¦...â€¦... (2)

Simplify the equation (2) for x

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