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: 2


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

Work Step by Step

Given: $\sinh x=\dfrac{4}{3}$ The remaining hyperbolic functions can be found as follows: Use the fact $\cosh^2 x-\sinh^2x=1$ or, $\cosh^2 x-(\dfrac{4}{3})^2=1 \\ or, \cosh^2 x=\dfrac{25}{9} $ Thus, $\cosh x= \dfrac{5}{3} \\ \tanh x= \dfrac{\sin hx}{\cosh x}=\dfrac{\dfrac{4}{3}}{\dfrac{5}{3}}=\dfrac{4}{5} $ Now, $sech x= \dfrac{1}{\cosh x}=\dfrac{1}{\dfrac{5}{3}}=\dfrac{3}{5} \\ csch x= \dfrac{1}{\sinh x}=\dfrac{1}{\dfrac{4}{3}}=\dfrac{3}{4} $ and $ coth x= \dfrac{1}{\tanh x}=\dfrac{1}{\dfrac{4}{5}}=\dfrac{5}{4}$
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