Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 10 - Conics, Parametric Equations, and Polar Coordinates - 10.4 Exercises - Page 722: 18

Answer

$$\left( {6,\frac{\pi }{4}} \right){\text{ and }}\left( { - 6,\frac{{5\pi }}{4}} \right)$$

Work Step by Step

$$\eqalign{ & {\text{We have the rectangular coordinates }}\left( {x,y} \right) = \left( {3\sqrt 2 ,3\sqrt 2 } \right) \cr & {\text{The polar coordinates are:}} \cr & r = \sqrt {{x^2} + {y^2}} \cr & r = \sqrt {{{\left( {3\sqrt 2 } \right)}^2} + {{\left( {3\sqrt 2 } \right)}^2}} \cr & r = 6 \cr & \tan \theta = \frac{{3\sqrt 2 }}{{3\sqrt 2 }} \cr & \theta = {\tan ^{ - 1}}\left( 1 \right) = \frac{\pi }{4} \cr & \theta = {\tan ^{ - 1}}\left( 1 \right) + \pi = \frac{{5\pi }}{4} \cr & {\text{Therefore, the polar coordinates are:}} \cr & \left( {6,\frac{\pi }{4}} \right){\text{ and }}\left( { - 6,\frac{{5\pi }}{4}} \right) \cr} $$
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