Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 11 - Cumulative Review Exercises - Page 1181: 14

Answer

See below:
1570764384

Work Step by Step

Consider the provided function, $ x=3\sin t $, $ y=4\cos t+2$ Consider the first function, $ x=3\sin t $ The interval is given from $ t=0$ to $ t=2\pi $. Therefore, put values of $ t $ in the function as $0\le t\le 2\pi $ Consider second function, $ y=4\cos t+2$ The interval is given from $ t=0$ to $ t=2\pi $. Therefore, put values of $ t $ in the function as $0\le t\le 2\pi $ For, $ t=\frac{\pi }{2}$ $\begin{align} & x=3\sin t \\ & =3\cdot \sin \frac{\pi }{2} \\ & =3 \end{align}$ And, $\begin{align} & y=4\cos \left( t+2 \right) \\ & =4\cos \left( \frac{\pi }{2}+2 \right) \\ & =2 \end{align}$ For, $ t=\pi $ $\begin{align} & x=3\sin t \\ & =3\cdot \sin \pi \\ & =0 \end{align}$ And, $\begin{align} & y=4\cos \left( t+2 \right) \\ & =4\cos \left( \pi +2 \right) \\ & =-2 \end{align}$ For, $ t=\frac{3\pi }{2}$ $\begin{align} & x=3\sin t \\ & =3\cdot \sin \frac{3\pi }{2} \\ & =-3 \end{align}$ And, $\begin{align} & y=4\cos \left( t+2 \right) \\ & =4\cos \left( \frac{3\pi }{2}+2 \right) \\ & =2 \end{align}$ For, $ t=0\text{ or 2}\pi $ $\begin{align} & x=3\sin t \\ & =3\cdot \sin 0 \\ & =0 \end{align}$ And, $\begin{align} & y=4\cos \left( t+2 \right) \\ & =4\cos \left( 0+2 \right) \\ & =6 \end{align}$
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