University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 7 - Section 7.3 - Hyperbolic Functions - Exercises - Page 417: 4


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

Work Step by Step

As we are given that $\cosh x=\dfrac{13}{5}$ Need to find all the hyperbolic functions. Use identity: $\cosh^2 x-\sinh^2x=1$ or, $(\dfrac{13}{5})^2-\sinh^2 x=1 \implies \sinh^2 x=\dfrac{144}{25}$ and $\sinh x= \dfrac{12}{5}$ Now, $\tanh x= \dfrac{\sin hx}{\cosh x}=\dfrac{\dfrac{12}{5}}{\dfrac{3}{15}}=\dfrac{12}{13}$ $sech x= \dfrac{1}{\cosh x}=\dfrac{1}{\dfrac{13}{5}}=\dfrac{5}{13}$; $csch x= \dfrac{1}{\sinh x}=\dfrac{1}{\dfrac{12}{5}}=\dfrac{5}{12}$; $coth x= \dfrac{1}{\tanh x}=\dfrac{1}{\dfrac{12}{13}}=\dfrac{13}{12}$
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