University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 3 - Section 3.5 - Derivatives of Trigonometric Functions - Exercises: 22

Answer

$\displaystyle s' = \frac{-1}{(1-cost)}=\frac{1}{cost-1}$

Work Step by Step

$\displaystyle s = \frac{sint}{1-cost}$ $\displaystyle s' = \frac{(1-cost)cost - sin^{2}t}{(1-cost)^{2}}$ $\displaystyle s' = \frac{cost-cos^{2}t-sin^{2}t}{(1-cost)^{2}}$ $\displaystyle s' = \frac{cost-1}{(1-cost)^{2}}$ $\displaystyle s' = \frac{-1}{(1-cost)}$
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