%Hyperbolic functions
%If you modify this file, please indicate here and in the footnote
%Math263B

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{\Large
Hyperbolic Functions and the Gateway Arch
\footnote{Copyright \copyright 2002 Steve Chapin.  All rights reserved.
Please address comments to young@math.ohiou.edu.}}
\end{center}

The Gateway Arch in St.\ Louis has the shape of an inverted
catenary.  Rising 630 feet at its center and streching 630 feet across
its base, the arch's shape can be described by  \\
$$
    y = -127.7 \cosh(x / 127.7) + 757.7 \verb$ for$ -315 \le x \le 315.
$$

\begin{enumerate}
\item Enter the following sequence of commands:
 \begin{enumerate}
      \item  \verb&syms x &
      \item  \verb&f = -127.7 * cosh(x / 127.7) + 757.7 &
      \item  \verb&ezplot(f, -315, 315)&
   \end{enumerate}
  Does the graph look like an arch?

\item  To compute the area beneath the Gateway Arch enter the
following sequence of commands:
\begin{enumerate}
    \item \verb& int(f, -315, 315) &
    \item \verb& double(ans) &
\end{enumerate}

\item  To compute the length of the Gateway Arch enter the
following sequence of commands:
\begin{enumerate}
    \item \verb& int(sqrt(1+diff(f)^2), -315, 315) &
    \item \verb& double(ans) &
\end{enumerate}
Are you surprised that the symbolic answer is expressed in terms of
exponential functions rather than hyperbolic functions?  Why or why
not?

\item On a separate piece of paper, prepare a brief written report
describing what happened and answering all the questions. Include the
results of all of the computations.  Use complete sentences and use 
standard mathematical notation. Do {\bf not} hand-in a printout.

\end{enumerate}

\vfill
\noindent

\textsf{Students may have little or no exposure to hyperbolic functions
in their calculus courses.  This assignment gives a real-life application
of hyperbolic functions.}

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