Trigonometry 7th Edition

Published by Cengage Learning
ISBN 10: 1111826854
ISBN 13: 978-1-11182-685-7

Chapters 1-8 - Cumulative Test - Page 477: 29

Answer

$r=\frac{2}{\cos\theta+\sin\theta}$.

Work Step by Step

To convert from polar to rectangular coordinates we use $x=r\cos\theta$ and $y=r\sin\theta$. To convert from rectangular to polar coordinates, we use $r=\pm\sqrt{x^2+y^2}$, $\tan\theta=\frac{y}{x}$, but aware of which quadrant the point lies in. Hence here $x+y=2\\r\cos\theta+r\sin\theta=2\\r(\cos\theta+\sin\theta)=2\\r=\frac{2}{\cos\theta+\sin\theta}$.
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