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: 49


$r=\frac{7}{3\cos \theta +\sin \theta }$.

Work Step by Step

The rectangular equation is: $3x+y=7$ …… (1) The relation between polar coordinates and rectangular coordinates is expressed as below: $x=r\cos \theta $ and $y=r\sin \theta $ …… (2) Substituting the values of $x\ \text{ and }\ y$ from (2) in (1), we get $\begin{align} & 3x+y=7 \\ & 3r\cos \theta +r\sin \theta =7 \\ & r\left( 3\cos \theta +\sin \theta \right)=7 \\ & r=\frac{7}{\left( 3\cos \theta +\sin \theta \right)} \end{align}$ Hence the obtained polar expression is $r=\frac{7}{3\cos \theta +\sin \theta }$.
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