Trigonometry 7th Edition

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

Chapter 8 - Test - Page 475: 24

Answer

$r=8\sin\theta$.

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 $x^2+y^2=8y\\r^2=8r\sin\theta\\r=8\sin\theta$.
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