Multivariable Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 0-53849-787-4
ISBN 13: 978-0-53849-787-9

Chapter 10 - Parametric Equations and Polar Coordinates - Review - Exercises - Page 710: 33

Answer

Points of intersection are: in polar coordinates: $(2,\pm \pi/3)$ in rectangular coordinates: $(1,\pm \sqrt 3)$

Work Step by Step

$r=2$ and $r =4 cos \theta$ will intersect when $2=4 cos \theta$ this implies that $cos \theta = \frac {1}{2}$ Co-ordinates of points of intersection are: $x=rcos\theta=2. \frac {1}{2}=1$ $y=rsin\theta=2. [\pm \frac {\sqrt 3}{2}]=\pm \sqrt 3$ Hence, points of intersection are: $(1,\pm \sqrt 3)$
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