Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 10 - Parametric Equations and Polar Coordinates - 10.3 Polar Coordinates - 10.3: 23

Answer

$r=\frac{1}{sin\theta-3cos\theta}$

Work Step by Step

$y=1+3x$ We know that: $sin\theta=y/r$, so $y=rsin\theta$ We also know that: $cos\theta=x/r$, so $x=rcos\theta$ Substituting for $x$ and $y$, we get: $rsin\theta=1+3rcos\theta$ $rsin\theta-3rcos\theta=1$ $r(sin\theta-3cos\theta)=1$ $r=\frac{1}{sin\theta-3cos\theta}$
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