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: 15

Answer

See image

Work Step by Step

Parametric equations: $\left\{\begin{array}{l} x=t\\ y=\sin t\\ z=2\cos t \end{array}\right.$ In the xy plane, (z=0) The projection is is $y=\sin x$, a sine curve. In the yz plane, (x=0) The projection is $y^{2}+\displaystyle \frac{z^{2}}{4}=1$, an ellipse. In the xz plane, (y=0) The projection is is $z=2\cos x$, a cosine curve with amplitude 2. This leads us to an elliptic cylinder along x, which has an elliptical helix that spirals along it.
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