This program is designed to compute the sine function using a power series. A very limited floating-point format is used to demonstrate some of the problems that can occur when using floating point.

The program computes each term in the power series and displays
the result. It continues computing terms until the last term is so small
that it doesn’t contribute to the final result. For comparison purposes,
the result of the library function `sin`

is displayed as well as the computed
sine.

The program is invoked by:

`sine `*value*

where *value* is an angle in radians. For
example, to compute sin(0) we use the command:

%x**1 0.000E+00 1! 1.000E+00 x**1/1! 0.000E+00 1 term computed sin(0.000E+00)= 0.000E+00 Actual sin(0)=0`sine 0`

And to compute sin(π) we use the command:

%x**1 3.141E+00 1! 1.000E+00 x**1/1! 3.141E+00 total 3.141E+00 x**3 3.099E+01 3! 6.000E+00 x**3/3! 5.165E+00 total -2.024E+00 x**5 3.057E+02 5! 1.200E+02 x**5/5! 2.548E+00 total 5.239E-01 x**7 3.016E+03 7! 5.040E+03 x**7/7! 5.985E-01 total -7.457E-02 x**9 2.976E+04 9! 3.629E+05 x**9/9! 8.201E-02 total 7.438E-03 x**11 2.936E+05 11! 3.992E+07 x**11/11! 7.355E-03 total 8.300E-05 x**13 2.897E+06 13! 6.227E+09 x**13/13! 4.652E-04 total 5.482E-04 x**15 2.858E+07 15! 1.308E+12 x**15/15! 2.185E-05 total 5.263E-04 x**17 2.819E+08 17! 3.557E+14 x**17/17! 7.927E-07 total 5.271E-04 x**19 2.782E+09 19! 1.217E+17 x**19/19! 2.287E-08 total 5.271E-04 x**21 2.744E+10 21! 5.109E+19 x**21/21! ...`sine 3.141`

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