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: 4

Answer

$\sinh x=\dfrac{12}{5} ;\\ \cosh x= \dfrac{3}{15} ;\\ \tanh x= \dfrac{12}{13} ; \\ sech x=\dfrac{5}{13} ; \\ csch x=\dfrac{5}{12} $ and $ coth x=\dfrac{13}{12}$

Work Step by Step

Given: $\cosh x=\dfrac{3}{15}$ The remaining hyperbolic functions can be found as follows: Use the fact: $\cosh^2 x-\sinh^2x=1$ or, $(\dfrac{3}{15})^2-\sinh^2 x=1$ or, $ \sinh^2 x=\dfrac{144}{25}$ or, $\sinh x= \dfrac{12}{5}$ and $\tanh x= \dfrac{\sin hx}{\cosh x}=\dfrac{\dfrac{12}{5}}{\dfrac{3}{15}}=\dfrac{12}{13}$ Now, $sech x= \dfrac{1}{\cosh x}=\dfrac{1}{\dfrac{13}{5}}=\dfrac{5}{13}$ $csch x= \dfrac{1}{\sinh x}=\dfrac{1}{\dfrac{12}{5}}=\dfrac{5}{12}$ and $coth x= \dfrac{1}{\tanh x}=\dfrac{1}{\dfrac{12}{13}}=\dfrac{13}{12}$
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