Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 13 - Section 13.1 - Vector Functions and Space Curves - 13.1 Exercises - Page 854: 24



Work Step by Step

The parametric equations of a circle having radius $r$ are; $x=r \cos t ; y =r \sin t$ Here, we have $x= \cos t , y=\sin t, z=\cos 2t$ We see tht $x$ and $y$ look like a circle when we look down from a top view with a high z-value. The parametric equation $z=t^2$ can be written as: $z=x^2$ This shows that the projection of the curve on the xz plane must be a circle of radius $1$ and the cosine function has a range of $[-1,1]$; that is $-1 \leq z \leq 1$ . This matches with $\bf{Graph{(I)}}$.
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