Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 10 - Parametric and Polar Curves - 10.2 Polar Coordinates - 10.2 Exercises - Page 729: 24

Answer

$$\left( {9,\pi } \right)$$ or $$\left( { - 9,2\pi } \right)$$

Work Step by Step

$$\eqalign{ & \left( { - 9,0} \right) \Rightarrow x = - 9{\text{ and }}y = 0 \cr & {\text{Converting to cartesian coordinates }}\left( {r,\theta } \right).{\text{ Where}} \cr & r = \sqrt {{x^2} + {y^2}} {\text{ and }}\theta = {\tan ^{ - 1}}\left( {\frac{y}{x}} \right) \cr & {\text{We obtain}}{\text{,}} \cr & r = \sqrt {{{\left( { - 9} \right)}^2} + {{\left( 0 \right)}^2}} = 9 \cr & {\text{Coordinate }}x{\text{ }}\left( {{\text{positive}}} \right){\text{, Coordinate }}y\left( {\text{0}} \right) \cr & \theta = {\tan ^{ - 1}}\left( {\frac{0}{{ - 9}}} \right) + \pi = \pi \cr & {\text{The polar coordinates are:}} \cr & \left( {r,\theta } \right) = \left( {9,\pi } \right) \cr & or \cr & \left( { - r,\theta + \pi } \right) = \left( { - 9,2\pi } \right) \cr} $$
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