Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 8 - Section 8.1 - Polar Coordinates - 8.1 Exercises - Page 593: 28

Answer

$(-\sqrt 3, 1)$

Work Step by Step

Step 1. Read the polar coordinates from the figure given in the Exercise: $r=2, \theta=\frac{5\pi}{6}$ Step 2. Convert from polar to rectangular coordinates: $x=r\cdot cos\theta=2cos\frac{5\pi}{6}=-2\times\frac{\sqrt 3}{2}=-\sqrt 3$ and $y=r\cdot sin\frac{5\pi}{6}=2\times1/2=1$ so the rectangular coordinates are $(-\sqrt 3, 1)$
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