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: 1

Answer

(a) and (e) label the same point (b) and (g) label the same point (c) and (h) label the same point (d) and (f) label the same point

Work Step by Step

Convert to rectangular coordinates, $(x,y)=(r\cos\theta,r\sin\theta).$ $\left[\begin{array}{rrrrrrrrr} & r & \theta & x=r\cos\theta & y=r\sin\theta & (x,y)\\ & & & & & \\ a. & 3 & 0 & 3 & 0 & (3,0)\\ b. & -3 & 0 & -3 & 0 & (-3,0)\\ c. & 2 & 2\pi/3 & -1 & \sqrt{3}/2 & (-1,\sqrt{3}/2)\\ d. & 2 & 7\pi/3 & 1 & \sqrt{3}/2 & (1,\sqrt{3}/2)\\ e. & -3 & \pi & 3 & 0 & (3,0)\\ f. & 2 & \pi/3 & 1 & \sqrt{3}/2 & (1,\sqrt{3}/2)\\ g. & -3 & 2\pi & -3 & 0 & (-3,0)\\ h. & -2 & -\pi/3 & -1 & \sqrt{3}/2 & (-1,\sqrt{3}/2) \end{array}\right]$ The pairs labeling the same point: (a) and (e) label the same point (b) and (g) label the same point (c) and (h) label the same point (d) and (f) label the same point
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