Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 8 - Polar Coordinates; Vectors - Section 8.1 Polar Cordinates - 8.1 Assess Your Understanding - Page 592: 71


$r^{2}\sin (2\theta)=1$

Work Step by Step

Substitute $x=r\cos\theta$, $y=r\sin\theta$ to obtain: $2xy=1\\ 2(r\cos\theta)(r\sin\theta)=1\\ r^{2}\times2\sin\theta\cos\theta=1$ Since $2\sin\theta \cos\theta=\sin (2\theta)$, we have $r^{2}\times2\sin\theta\cos\theta=1\\ r^{2}\sin (2\theta)=1$
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