Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 16 - Vector Calculus - 16.6 Parametric Surfaces and Their Areas - 16.6 Exercises - Page 1160: 17


Plot $III$

Work Step by Step

Given : $x=cos^{3}u cos^{3}v$ $y=sin^{3}u cos^{3}v$ $z=sin^{3}v$ To find the grid curves corresponding to $u$ as constant , substitute $v=k$ $x=cos^{3}u cos^{3}k$ $y=sin^{3}u cos^{3}k$ $z=sin^{3}k$ This represents a family of astroid parallel to $xy$ plane with parameter $a=cos^{3}k$ Only Plot $III$ contains astroid as grid curves.
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