Single Variable Calculus, Chapter 7, 7.7, Section 7.7, Problem 4

Determine the numerical value of a.) $\cos h 3$ and b.) $\cos h (\ln 3)$

a.) $\cos h 3$

Using Hyperbolic Function


$
\begin{equation}
\begin{aligned}

\cos h x =& \frac{e^x + e^{-x}}{2}
\\
\\
\cos h 3 =& \frac{e^3 + e^{-3}}{2}
\\
\\
\cos h 3 =& \frac{\displaystyle e^3 + \frac{1}{e^3}}{2}
\\
\\
\cos h 3 =& \frac{e^6 + 1}{2e^3}
\\
\\
\cos h 3 =& 10.067662


\end{aligned}
\end{equation}
$


b.) $\cos h (\ln 3)$

Using Hyperbolic Function


$
\begin{equation}
\begin{aligned}

\cos h x =& \frac{e^x + e^{-x}}{2}
\\
\\
\cos h(\ln 3) =& \frac{e^{\ln 3} + e^{- \ln 3}}{2}
\\
\\
\cos h(\ln 3) =& \frac{\displaystyle e^{\ln 3} + \frac{1}{e^{\ln 3}}}{2}
\\
\\
\cos h(\ln 3) =& \frac{\displaystyle 3 + \frac{1}{3}}{2}
\\
\\
\cos h(\ln 3) =& \frac{\displaystyle \frac{9 + 1}{3}}{2}
\\
\\
\cos h(\ln 3) =& \frac{10}{2(3)}
\\
\\
\cos h(\ln 3) =& \frac{10}{6}
\\
\\
\cos h(\ln 3) =& \frac{5}{3}

\end{aligned}
\end{equation}
$