Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 14 - Multiple Integrals - 14.4 Surface Area; Parametric Surfaces - Exercises Set 14.4 - Page 1036: 17

Answer

$x=u, \quad \sin u \cos v =y\quad \sin u \sin v=z$ is a parametrization for the surface resulting from $\sin x=y$ about the $x$ axis.

Work Step by Step

Our function is $\sin x=y$ Since we revolved this function about the $x$ axis, $x$ is a free parameter, ie. we can take $u=x,$ and then \[ \sin u \cos v =y \text { and } \sin u \sin v=z \] $x=u, \quad \sin u \cos v =y\quad \sin u \sin v=z$ is a parametrization for the surface resulting from $\sin x=y$ about the $x$ axis.
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