Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 6 - Section 6.3 - Polar Coordinates - Exercise Set - Page 743: 73

Answer

The rectangular equation is, $xy=1$

Work Step by Step

Using, $r\cos \theta =x$, and $r\sin \theta =y$ we will convert the polar equation to the rectangular equation. Therefore, $\begin{align} & {{r}^{2}}\sin 2\theta =2 \\ & 2{{r}^{2}}\sin \theta \cos \theta =2 \\ & r\sin \theta \times r\cos \theta =1 \\ & xy=1 \end{align}$ Hence, the rectangular equation of ${{r}^{2}}\sin 2\theta =2$ is $xy=1$.
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