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: 14

Answer

$\left( {2\sqrt 5 ,5.8195} \right)$

Work Step by Step

$$\eqalign{ & {\text{We have the rectangular coordinates }}\left( {x,y} \right) = \left( {4, - 2} \right) \cr & {\text{The polar coordinates are:}} \cr & r = \sqrt {{x^2} + {y^2}} \cr & r = \sqrt {{{\left( 4 \right)}^2} + {{\left( { - 2} \right)}^2}} \cr & r = 2\sqrt 5 \cr & \tan \theta = \frac{{ - 2}}{4} \cr & \theta = {\tan ^{ - 1}}\left( {\frac{{ - 2}}{4}} \right) \cr & \theta = {\tan ^{ - 1}}\left( {\frac{{ - 2}}{4}} \right) + 2\pi \approx 5.8195 \cr & {\text{Therefore}}{\text{, the polar coordinate is:}} \cr & \left( {2\sqrt 5 ,5.8195} \right) \cr} $$
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