Thomas' Calculus 13th Edition

by Thomas Jr., George B.

Published by Pearson

ISBN 10: 0-32187-896-5

ISBN 13: 978-0-32187-896-0

Chapter 13: Vector-Valued Functions and Motion in Space - Section 13.3 Arc Length in Space - Exercises 13.3 - Page 760: 19

Answer

$ y=sint-tcost $

Work Step by Step

PQB=QOB=t and PQ=arc(AQ)=t since PQ=length of unwound string=length of arc(AQ); thus; x=OB+BC=OB+DP=cost+tsint so the parametric equation is; y=PC=QB-QD=sint-tcost

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