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 687: 33

Answer

See image below.

Work Step by Step

First, define r as a function of $\theta$ $ r=f(\theta)=-2\sin\theta$ Then build a table of values for $\theta=0,\pi/6,\pi/3,...$ and for each $\theta$ calculate x coordinate = $ f(\theta)\cdot\cos\theta,\qquad y=f(\theta)\cdot\sin\theta$ Plot the points and join with smooth curve. (Work done in geogebra.)
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