Multivariable Calculus, 7th Edition

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

Chapter 13 - Vector Functions - 13.1 Exercises - Page 870: 10

Answer

See image

Work Step by Step

Parametric equations: $\left\{\begin{array}{l} x=\sin\pi t\\ y=t\\ z=\cos\pi t \end{array}\right.$ Build a table of values for t, -1, -0.75, -0.5, ... and calculate the coordinates and plot the points. The arrow indicates the direction in which t increases. Also, since $\sin^{2}A+\cos^{2}A=1, $we note that all the points (x,y,z) lie on the surface $x^{2}+z^{2}=1,$ a cylinder along the y axis, with radius 1. The curve is a helix that spirals around this cylinder.
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