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: 52

Answer

$(\sqrt{13},213.7^\circ)$

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 the given point in polar coordinates using a calculator: $(\pm(\sqrt{(-3)^2+(-2)^2},\tan^{-1}\frac{-2}{-3})=(\sqrt{13},213.7^\circ)$
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