LBS290F                                                     Spring 1992

                        ASSIGNMENT 3 - Taylor Series

****** REVISED VERSION - Thanks to Dr. Hamelink *********

Due Date: April 8, 1992 11:59PM

This program will calculate a simple Taylor Approximation for the SIN 
function from trigonometry.

The Taylor approximation of the SIN function is an infinite series expressed
by the following summation:

                   oo
                 ------                   (2i - 1)
                 \            (i+1)     X
    sin(x)   =    >       (-1)       ---------------
                 /                      (2i - 1) !
                 ------
                  i = 1

On computers to approximate the SIN function, some fixed number of the terms
of this sum are computed.  As more terms of the sum which are used, 
the more accurate the approximation will become.  For example if three
terms of the Taylor Series are used, the approximation will be:

                          3         5  
           ~             X         X    
   sin(x)  =     X  -  -----  +  -----
                         3!        5!

If five terms of the Taylor Series were used the approximation would be:

                          3         5         7         9 
           ~             X         X         X         X   
   sin(x)  =     X  -  -----  +  -----  -  -----  +  -----
                         3!        5!        7!        9! 

Your program will prompt for a value for X between 0 and 2.0.  The program
will then compute the actual value for SIN(X) using the intrinsic function
SIN in FORTRAN. The program will also calculate the Taylor approximation
for SIN using 2, 3, and 4 terms.  The program will print out the actual
SIN and both approximations.  The program will also print out the difference
between the actual value for SIN(X) and each of the approximations.

Example execution:

  $ a.out
   Enter X
  1.5
   X is   1.50000000 
   SIN(X) is   9.974949956E-001 
   Taylor approximation using 2 terms is   9.375000000E-001 
   Error using 2 terms is  -5.999499559E-002 
   Taylor approximation using 3 terms is   1.00078130 
   Error using 3 terms is   3.286302090E-003 
   Taylor approximation using 4 terms is   9.973912239E-001 
   Error using 4 terms is  -1.037716866E-004 
  $ 

Hint:  Use the value for 2 terms of the Taylor series to computer the
3 term value.  Use the 3 term value to compute the 4 term value.

Note:  n! = 1 x 2 x 3 ... x n-1 x n        5! = 1 x 2 x 3 x 4 x 5 = 120