Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 10 - Analytic Geometry - 10.7 Plane Curves and Parametric Equations - 10.7 Assess Your Understanding - Page 695: 39


$\begin{cases} x=2\cos (-\pi t)\\ y=3\sin (-\pi t) \end{cases}$ with $0\leq t\leq 2$

Work Step by Step

We are given the ellipse: $\dfrac{x^2}{4}+\dfrac{y^2}{9}=1$ Graph the ellipse: When $t=0$, the motion begins from $(2,0)$; therefore, for $t=0$ we have: $x=2$ $y=0$ Therefore a parametric set of equations for the ellipse is: $\begin{cases} x=2\cos (\omega t)\\ y=3\sin (\omega t) \end{cases}$ When $t$ increases, $x$ decreases and $y$ decreases; therefore $\omega<0$. Determine $\omega$ using the revolution: $\dfrac{2\pi}{|\omega|}=2$ $\omega=-\pi$ The parametric set of equations is: $\begin{cases} x=2\cos (-\pi t)\\ y=3\sin (-\pi t) \end{cases}$ with $0\leq t\leq 2$
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