Answer
(a)$\qquad 10.018$
(b)$\qquad-0.964$
Work Step by Step
Definitions
$\displaystyle \sinh x=\frac{e^{x}-e^{-x}}{2} \qquad \mathrm{c}\mathrm{s}\mathrm{c}\mathrm{h}\ x=\displaystyle \frac{1}{\sinh x},x\neq 0$
$\displaystyle \cosh x=\frac{e^{x}+e^{-x}}{2} \qquad \mathrm{s}\mathrm{e}\mathrm{c}\mathrm{h}\ x=\displaystyle \frac{1}{\cosh x}$
$\displaystyle \tanh x=\frac{\sinh x}{\cosh x} =\frac{e^{x}-e^{-x}}{e^{x}+e^{-x}} \qquad \coth x=\frac{1}{\tanh x},x\neq 0$
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(a)
$\displaystyle \sinh 3=\frac{e^{3}-e^{-3}}{2}\approx 10.018$
(b)
$\tanh (- 2 )=\displaystyle \frac{\sinh(-2)}{\cosh(-2)}=\frac{e^{-2}-e^{2}}{e^{-2}+e^{2}}\approx-0.964$
