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: 9

Answer

$y=1-2x^{2},\ \ x\in[-1,1]$

Work Step by Step

From the parametric equation for x, we see that $x\in[-1,1].$ Using a double angle identity formula for cosine, $\cos 2t=1-2\sin^{2}t$ substituting, $y=1-2x^{2}\quad $... (a parabola that opens down) From the parametric equation for x, we see that $x\in[-1,1],$ so we restrict the Cartesian equation: $y=1-2x^{2},\ \ x\in[-1,1]$ 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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