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: 3

Answer

$(a)$ $(2,\ \pi/2+2k\pi),\ k\in \mathbb{Z}$ or $(-2,\ \pi/2+(2k+1)\pi),\ k\in \mathbb{Z}$ $(b)$ $(2,\ 0+2k\pi),\ k\in \mathbb{Z}$ or $(-2,\ 0+(2k+1)\pi),\ k\in \mathbb{Z}$ $(c)$ $(-2,\ \pi/2+2k\pi),\ k\in \mathbb{Z}$ or $(+2,\ \pi/2+(2k+1)\pi),\ k\in \mathbb{Z}$ $(d)$ $(-2,\ 0+2k\pi),\ k\in \mathbb{Z}$ or $(+2,\ 0+(2k+1)\pi),\ k\in \mathbb{Z}$ .

Work Step by Step

Plotting $(r,\theta):$ - if $r$ is positive, then the point lies on the terminal side of $\theta+2k\pi,\ k\in \mathbb{Z}$ - if $r$ is negative, then the point lies opposite the terminal side of $\theta$; it lies on the terminal side of $\theta\pm\pi+2k\pi=\theta+ (2k+1)\pi,\ k\in \mathbb{Z}$ $(a)$ $(2,\ \pi/2+2k\pi),\ k\in \mathbb{Z}$ or $(-2,\ \pi/2+(2k+1)\pi),\ k\in \mathbb{Z}$ $(b)$ $(2,\ 0+2k\pi),\ k\in \mathbb{Z}$ or $(-2,\ 0+(2k+1)\pi),\ k\in \mathbb{Z}$ $(c)$ $(-2,\ \pi/2+2k\pi),\ k\in \mathbb{Z}$ or $(+2,\ \pi/2+(2k+1)\pi),\ k\in \mathbb{Z}$ $(d)$ $(-2,\ 0+2k\pi),\ k\in \mathbb{Z}$ or $(+2,\ 0+(2k+1)\pi),\ k\in \mathbb{Z}$
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