(C) Copyright 1994 D.C.M. Burbulla and  C.T.J. Dodson
       Notebook to support the book
     Self-Tutor for Computer  Calculus

Using Mathematica 2

by
     D. C. M. Burbulla and C. T. J. Dodson, University of Toronto
 Published by:    
    Prentice-Hall Canada  (English)   ISBN 0130152803     and 
     Prentice-Hall Japan  (Japanese) ISBN4-8101-8558-3 C3055 P2880E

Trigonometric and Hyperbolic Functions

We make some suggestions for exploring these functions. You should first
plot all these new functions and decide where they are increasing, decreasing,
critical, undefined. Decide also where they have inverse functions defined.
Note that there is a special package to help with trigonometric identities; you
can call this in with:

<< Algebra/Trigonometry.m

?TrigReduce

Chap11.m

in[n_] := n/2 (Sin[2 Pi/n])  (* Inscribed n-gon area *)

 ex[n_] := n (Tan[Pi/n])  (* Exscribed n-gon area *)

We look at the plots of these functions, which give the areas of the inscribed
and the exscribed polygons of n sides for a unit circle.

ListPlot[Table[n/2(Sin[2 Pi/n]) ,{n,4,100}],
                   AxesLabel->{"n",""}];

ListPlot[Table[n(Tan[Pi/n]) ,{n,4,100}],
                   AxesLabel->{"n",""}];

Show[%,%%];

It is always a good idea to look at series expansions of new functions:

Series[Sin[x],{x,0,10}]

Series[Cos[x],{x,0,10}]

Series[Tan[x],{x,0,10}]

Do the same series investigation for the other trigonometric and hyperbolic
functions..