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: 10

Answer

The curve is an Helix winding around the \(y\)-axis.

Work Step by Step

\[ x(t) = \sin (\pi t) \\ z(t) = \cos(\pi t) \] Describe a circle oriented on the \(xy\)-plane. When we set \(y(t) = t\) it becomes an Helix that goes towards the \(y\)-axis.
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