Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 10 - Section 10.3 - Polar Coordinates - 10.3 Exercises - Page 666: 2

Answer

(a) We can see the point $(2,\frac{5\pi}{6})$ on the graph. Two other pairs of polar coordinates are $(2, \frac{17\pi}{6})$ and $(-2, \frac{11\pi}{6})$ (b) We can see the point $(1,-\frac{2\pi}{3})$ on the graph. Two other pairs of polar coordinates are $(1, \frac{4\pi}{3})$ and $(-1, \frac{\pi}{3})$ (c) We can see the point $(-1,\frac{5\pi}{4})$ on the graph. Two other pairs of polar coordinates are $(1, \frac{\pi}{4})$ and $(-1, \frac{13\pi}{4})$

Work Step by Step

(a) We can see the point $(2,\frac{5\pi}{6})$ on the graph. We can find two other pairs of polar coordinates: $(2, \frac{5\pi}{6}+2\pi) = (2, \frac{17\pi}{6})$ $(-2, \frac{5\pi}{6}+\pi) = (-2, \frac{11\pi}{6})$ (b) We can see the point $(1,-\frac{2\pi}{3})$ on the graph. We can find two other pairs of polar coordinates: $(1, -\frac{2\pi}{3}+2\pi) = (1, \frac{4\pi}{3})$ $(-1, -\frac{2\pi}{3}+\pi) = (-1, \frac{\pi}{3})$ (c) We can see the point $(-1,\frac{5\pi}{4})$ on the graph. We can find two other pairs of polar coordinates: $(1, \frac{5\pi}{4}-\pi) = (1, \frac{\pi}{4})$ $(-1, \frac{5\pi}{4}+2\pi) = (-1, \frac{13\pi}{4})$
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