Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 8 - Section 8.2 - Graphs of Polar Equations - 8.2 Exercises - Page 601: 57

Answer

See graph and explanations.

Work Step by Step

Step 1. Convert the equation into polar form using $x^2+y^2=r^2, x=r\cdot cos\theta, y=r\cdot sin\theta$ we have $r^6=4r^2cos^2\theta r^2sin^2\theta$ which leads to $r^2=4sin^2\theta cos^2\theta=(sin2\theta)^2$, thus $r=\pm sin2\theta$ Step 2. As the graph of $r=sin2\theta$ is the same as $r=-sin2\theta$, we graph the first function as shown in the figure.
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