Evaluating Hyperbolic Functions

Find the exact value of:

1. \(\cosh 0\)
2. \({\mathop{\rm{sech}}}~0\)
3. \(\tanh ( \ln 2) \)

Solution

(a) \(\cosh 0=\dfrac{e^{0}+e^{0}}{2}=\dfrac{2}{2}=1\)

(b) \({\mathop{\rm{sech}}}~0=\dfrac{1}{\cosh 0}=\dfrac{1}{1}=1\)

(c) \(\tanh ( \ln 2) =\dfrac{e^{\ln 2}-e^{-\ln 2}}{e^{\ln 2}+e^{-\ln 2}}=\dfrac{2-e^{\ln ( 1/2) }}{2+e^{\ln ( 1/2) }}=\dfrac{2-\dfrac{1}{2}}{2+\dfrac{1}{2}}=\dfrac{3}{5}\)