Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 7 - Exponential Functions - 7.9 Hyperbolic Functions - Exercises - Page 384: 6


$$\cosh x=\frac{\sqrt{41}}{5}\quad \tanh x= \frac{4}{\sqrt{41}} .$$

Work Step by Step

Since, $\sinh x=0.8=\frac{4}{5}$, then using the property $$\cosh^2x-\sinh^2x=1\Longrightarrow \cosh x=\frac{\sqrt{41}}{5}.$$ Now, $$\tanh x=\frac{\sinh x}{\cosh x}=\frac{4}{\sqrt{41}}.$$
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