University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 10 - Section 10.1 - Parametrizations of Plane Curves - Exercises - Page 562: 5

Answer

$x^{2}+y^{2}=1$

Work Step by Step

Square both parametric equations: $x^{2}=\cos^{2}2t$ $y^{2}=\sin^{2}2t$ Add the two equations: $x^{2}+y^{2}=1$ To graph, create a function value table using values for t, in ascending order of t, calculating the x- and y-coordinates of points on the graph. Plot and join the points obtained with a smooth curve, noting the direction in which t increases.
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