Precalculus (6th Edition) Blitzer

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

Chapter 6 - Section 6.4 - Graphs of Polar Equations - Exercise Set - Page 755: 83

Answer

The number of loops increase as the value of n increases. When the value of n is odd, there are the same number of loops as the number n and for $\theta \,\max \,=\,\pi $, the polar equation traces the graph only once. When the value of n is even, there are twice the number of loops as the number n and for $\theta \,\max \,=\,2\pi $, the polar equation traces the graph only once.
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Work Step by Step

From the graphs, it can be observed that $\sin \,n\theta $ increases its number of loops with increase in the value of n. The number of loops increase with increase in the value of n. For odd values of n, there are the same number of loops as the number n and for $\theta \,\max \,=\,\pi $, the polar equation traces the graph only once. For the even values of n, there are twice the number of loops as the number n and for $\theta \,\max \,=\,2\pi $, the polar equation traces the graph only once.
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