   Chapter 10.2, Problem 69E

Chapter
Section
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=cosθ and y=sin2θ,0θπ

x=cos(θ) and y=sin2(θ),0θπ

Explanation:

Consider the given parametric equations.

x=cosθ and y=sin2θ,0θπ …...…... (1)

x=cos(θ) and y=sin2(θ),0θπ …...…... (2)

Simplify the equation (2) for x

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