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 754: 5


The polar equation of the given polar curve is $r=3\sin 3\theta $.

Work Step by Step

From the given polar curve we can observe that it is a rose curve. In case of a rose curve of $n$ number of petals (where $n$ is odd), the general form of the polar equation will be either $r=a\sin n\theta $ or $r=a\cos n\theta $, $a>0$. Hence, for $\text{3 petals}$, $n$ will be $3$. And on the basis of the graph, For, $\theta =\frac{\pi }{6}$ $r=3$ And, For, $\theta =0$ $r=0$ By applying the above condition, it is concluded that the polar equation for the graph will be $r=3\sin 3\theta $.
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