Trigonometry 7th Edition

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

Chapter 8 - Section 8.5 - Polar Coordinates - 8.5 Problem Set - Page 458: 33

Answer

$(-6,-2\sqrt3)$

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 $r=\pm\sqrt{x^2+y^2}$, $\tan\theta=\frac{x}{y}$, but aware of which quadrant the point lies in. Hence here the given point in rectangular coordinates: $(-4\sqrt3\cos(\pi/6),-4\sqrt3\sin(\pi/6))=(-6,-2\sqrt3)$
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