Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 10 - Section 10.3 - Polar Coordinates - 10.3 Exercises - Page 667: 26



Work Step by Step

We are given that $x^2-y^2=4$. Using the cartesian-to-polar substitutions of $x=rcos\theta$ and $y=rsin\theta$, we can rewrite the expression as $(rcos\theta)^2-(rsin\theta)^2=4$. This can be rewritten as $r^2cos^2\theta-r^2sin^2\theta=4$. Factoring out an $r^2$, we get $r^2(cos^2\theta-sin^2\theta)=4$. Using the double-angle identity for cosine, we get $r^2cos\,2\theta=4$.
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