University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 10 - Section 10.3 - Polar Coordinates - Exercises - Page 577: 20

Answer

Graph: .

Work Step by Step

Plotting points $(r,\theta)$, $r$ is the directed distance of the point from the pole. $\theta$ defines the angle of the ray on which the point lies, - remains $\theta$ when $r$ is positive - becomes $\theta\pm\pi$ when $r$ is negative The region is such that: the angle $\pi/2$ terminates on the +y axis (Cartesian), and defines a line through the pole (the origin) with slope $\tan( \pi/2) =$undefined (the y-axis). Since only negative $r$'s are considered, only the points on the -y-axis are represented.
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