Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 7: Transcendental Functions - Section 7.7 - Hyperbolic Functions - Exercises 7.7 - Page 431: 61

Answer

$\displaystyle \ln(\frac{2}{3})$

Work Step by Step

Substitute into the relevant formula: $\displaystyle \sinh^{-1}(-\frac{5}{12})=\ln(-\frac{5}{12}+\sqrt{\frac{25}{144}+1})$ $=\displaystyle \ln(-\frac{5}{12}+\sqrt{\frac{169}{144}})$ $=\displaystyle \ln(-\frac{5}{12}+\frac{13}{12})$ $=\displaystyle \ln(\frac{8}{12})$ =$\displaystyle \ln(\frac{2}{3})$
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