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 430: 1


$\sinh x=\dfrac{-3}{4}\\ \cosh x= \dfrac{5}{4}\\ \tanh x= \dfrac{-3}{5} \\ sech x=\dfrac{4}{5} \\ csch x=\dfrac{-4}{3}$ and $ coth x=\dfrac{-5}{3}$

Work Step by Step

Given: $\sinh x=\dfrac{-3}{4}$ The remaining hyperbolic functions can be found as follows: Use the fact $\cosh^2 x-\sinh^2x=1$ or, $\cosh^2 x-(\dfrac{-3}{4})^2=1 \\ or, \cosh^2 x=\dfrac{25}{16} $ Thus, $\cosh x= \dfrac{5}{4} \\ \tanh x= \dfrac{\sin hx}{\cosh x}=\dfrac{\dfrac{-3}{4}}{\dfrac{5}{4}}=\dfrac{-3}{5} and \\ sech x= \dfrac{1}{\cosh x}=\dfrac{1}{\dfrac{5}{4}}=\dfrac{4}{5} \\ csch x= \dfrac{1}{\sinh x}=\dfrac{1}{\dfrac{-3}{4}}=\dfrac{-4}{3} \\ coth x= \dfrac{1}{\tanh x}=\dfrac{1}{\dfrac{-3}{5}}=\dfrac{-5}{3}$
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