Multivariable Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 0-53849-787-4
ISBN 13: 978-0-53849-787-9

Chapter 10 - Parametric Equations and Polar Coordinates - 10.3 Exercises - Page 688: 69

Answer

$\theta\in[0,2\pi]$

Work Step by Step

Work done in geogebra: First, define r as a function of $\theta$ Use x = $ f(\theta)\cdot\cos\theta,\qquad y=f(\theta)\cdot\sin\theta$ to plot the curve. Change the domain until the curve retraces itself. Here, $\theta\in[0,2\pi]$ The points A, B, C show the direction in which the parameter increases.
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