\magnification=\magstep1
\nopagenumbers
\font\bigrm=cmr17
\font\medrm=cmr10 scaled\magstep2

\def\cosh{{\rm c}}
\def\sinh{{\rm s}}
\def\tanh{{\rm t}}
\def\coth{{\rm ct}}
\def\sech{{\rm sc}}
\def\csch{{\rm cs}}

\centerline{\bigrm Trigonometric-Like Functions}
\bigskip

\noindent
{\bf Purpose:}
The purpose of this project is to introduce you to some functions
which are similar to the trigonometric functions.
\bigskip

\noindent
{\bf Procedure:}  You are to follow the steps below.  You do not need to
do the steps in exactly the order indicated as long as you cover
everything you are asked to do.
After completing the outline below you should write your
results and calculations {\bf neatly}.  Be sure to include relevant
graphs in what you turn in. Your grade will be determined
in part by your presentation.
\bigskip

\noindent
{\bf Project Outline:}
\item{1.}Define $\cosh(x)={e^x+e^{-x}\over 2}$ and
         $\sinh(x)={e^x-e^{-x}\over 2}$.  Think of these functions as
         playing the role of $\cos$ and $\sin$ and define the functions
         $\tanh$, $\coth$, $\sech$, and $\csch$ which should play the
         roles of $\tan$, $\cot$, $\sec$, and $\csc$.
         Graph each and find the
         range and domain of each function.
\item{2.}Derive formulas corresponding to $\sin^2x+\cos^2x=1$,
         $\tan^2x+1=\sec^2x$, and $\cot^2x+1=\csc^2x$ for the functions
         defined in Part~1.  Graph the set of points of the form
         $(\cosh(t),\sinh(t))$ where $-10<t<10$ using Mathematica and
         relate the graph to one of the formulas you derived.
\item{3.}Derive formulas for $\sinh$ and $\cosh$ which correspond
         to the sum of two angle formulas of the trig functions.
\item{4.}Derive formulas for the inverse functions for $\sinh$ and
         $\cosh$.
\bye