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: 84

Answer

As the value of n increases, the number of loops of $\cos n\theta $ increases. If n is odd, there are n loops and $\theta \,\max \,=\,\pi $ traces the graph once, while if n is even, there are 2n loops and $\theta \,\max \,=\,2\pi $ traces the graph once. Yes, the conclusions are the same as for $\sin \,n\theta $.
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Work Step by Step

From the graphs, it can be observed that the number of loops of $\cos n\theta $ increases with increase in the value of n. If n is odd, there are n loops and $\theta \,\max \,=\,\pi $ traces the graph once, while if n is even, there are 2n loops and $\theta \,\max \,=\,2\pi $ traces the graph once. Yes, the conclusions are the same as for $\sin \,n\theta $.
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