Well, you should just specify the range of validity of your expansion.
Expansion used in your routine
'Approximation is x - ( x**3 / 3! ) + ( x**5 / 5! ) - ( x**7 / 7! ) + ...'
is valid only around x=0.
Around some arbitrary value of x=a, you should make expansion
sin(x)=sin(a)+(x-a)*sin'(x|x=a)/1!+(x-a)^2*sin''(x|x=a)/2!+...
(where sin''(x|x=a) means second derivation of function sin(x) for x=a
etc.)
Here is a bit more specific Taylor series for sin(a+x):
sin(a+x)=sin(a)+x*cos(a)-x^2*sin(a)/2!-x^3*cos(a)/3!+x^4*sin(a)/4!+...+x^n*sin(a+n*PI/2)/n!
where you can specify values of sin(a) at the points of mesh (of
wanted density - the finer, the better) in the table (proposed before)
and then use expansion above to get values of sin() around that point.
Analogy can be used for cos(x).
Regards,
Danko Radic
Dept. of Physics
University of Zagreb
Croatia
------------------------------------------------------------
On Thu, 8 Apr 1999, Creative Digital Publishing Inc. wrote:
> >> I have been trying to use cosine and sine in my application.
> >> I have tried to use math.h but this doesn't seem to be a palmfile.
> >> Does anyone have a suggestion?
>
> Here's some code that's worked fine for me. Hope it helps.
>
> Regards,
> Steve Mann
>
> # # #
>
> #define MINUS_ONE ( double ) -1.0
> #define DEGS360_RADIANS 360.0 * DEGREES_TO_RADS
> #define MAX_COS_ITERATIONS 10
> #define MAX_SIN_ITERATIONS 10
>
> /*****************************************************
> __sin
>
> Calculate the sin of a double radians angle.
> Approximation is x - ( x**3 / 3! ) + ( x**5 / 5! ) - ( x**7 / 7! ) + ...
> *****************************************************/
>
> double __sin ( double x ) {
>
> double result, numerator, denominator, term, sign, factorial, x1;
> int cnt = 0;
>
> // scale input angle to proper range of values
>
> x1 = x;
> while ( x1 > DEGS360_RADIANS ) {
> x1 = x1 - DEGS360_RADIANS;
> }
>
> // initialize everything
>
> result = x1;
> numerator = x1;
> denominator = ONE;
> factorial = ONE;
> sign = MINUS_ONE;
>
> for ( cnt = 0; cnt < MAX_SIN_ITERATIONS; cnt++ ) {
>
> // calculate the next term
>
> numerator = numerator * x1 * x1;
> denominator = denominator * ( factorial + ONE ) * (
> factorial + TWO );
> term = numerator / denominator;
> result = result + ( sign * term ) ;
>
> // prepare for next sequence thru loop
>
> sign = sign * MINUS_ONE;
> factorial = factorial + TWO;
> }
>
> return result;
> }
>
>
> /*****************************************************
> __cos
>
> Calculate the cos of a double radians angle
> Approximation is 1 - ( x**2 / 2! ) + ( x**4 / 4! ) - ( x**6 / 6! ) + .....
> *****************************************************/
>
> double __cos ( double x ) {
>
> double result, numerator, denominator, term, sign, factorial, x1;
> int cnt = 0;
>
>
> // scale input angle to proper range of values
>
> x1 = x;
> while ( x1 > DEGS360_RADIANS ) {
> x1 = x1 - DEGS360_RADIANS;
> }
>
> // initialize everything
>
> result = ONE;
> numerator = x1 * x1;
> denominator = TWO;
> factorial = TWO;
> sign = MINUS_ONE;
>
> for ( cnt = 0; cnt < MAX_COS_ITERATIONS; cnt++ ) {
>
> // calculate the next term
>
> term = numerator / denominator;
> result = result + ( sign * term ) ;
>
> // prepare for next sequence thru loop
>
> numerator = numerator * x1 * x1;
> denominator= denominator * ( factorial + ONE ) * (
> factorial + TWO );
> factorial = factorial + TWO;
> sign = -sign;
> }
>
> return result;
> }
>
> -------------------------------------------
> Creative Digital Publishing Inc.
> 1317 Palm Street, San Luis Obispo, CA 93401-3117
> -------------------------------------------
> 805.788.0138 805.593.3811 (fax)
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>
>
>
>
