Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 12 - Parametric Equations, Polar Coordinates, and Conic Sections - 12.3 Polar Coordinates - Exercises - Page 617: 5


a) $(\frac{3\sqrt 3}{2},\frac{3}{2})$ b) $(-3\sqrt 2, 3\sqrt 2)$ c) $(0,0)$ d) $(0, -5)$

Work Step by Step

Recall: The $x$ and $y$ coordinates in a rectangular coordinate system are given by $x= r\cos\theta$ and $y= r\sin\theta$. Thus, we have: a) $x= 3\cos\frac{\pi}{6}=\frac{3\sqrt 3}{2}$ $y= 3\sin\frac{\pi}{6}=3\times\frac{1}{2}=\frac{3}{2}$ $(x,y)=(\frac{3\sqrt 3}{2},\frac{3}{2})$ b) $x=6\cos\frac{3\pi}{4}=6\times-\frac{1}{\sqrt 2}=-3\sqrt 2$ $y=6\sin\frac{3\pi}{4}=6\times\frac{1}{\sqrt 2}=3\sqrt 2$ $(x,y)=(-3\sqrt 2, 3\sqrt 2)$ c) $x= 0\cos\frac{\pi}{5}=0$ $y=0\sin\frac{\pi}{5}=0$ $(x,y)=(0,0)$ d) $x= 5\cos(-\frac{\pi}{2})=5\times0=0$ $y=5\sin(-\frac{\pi}{2})=5\times(-1)=-5$ $(x,y)=(0, -5)$
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