Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 3 - Section 3.11 - Hyperbolic Functions - 3.11 Exercises: 7

Answer

sinh(-x) = -sinh(x)

Work Step by Step

Use the definition of hyperbolic sine. Then, find $\sinh{(-x)}$ and factor out a negative sign. $$sinh(x) = \frac{e^{x} - e^{-x}}{2}$$ sinh(-x) = $\frac{e^{-x} - e^{-(-x)}}{2}$ = $\frac{e^{-x} - e^{-x}}{2}$ = $\frac{-(e^{x} - e^{-x})}{2}$ = -sinh(x)
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