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Alireza_M · (This post was last modified: 12-31-2009 08:56 AM by Alireza_M.)

this program will calculate cosinus of a favorite degree with favorite Taylor expansion numbers involved,and will compare it with the original cosinus
function,heres the code(Note:the cosinus has been calculated around zero,this is popular as McLauren expansion):

Code:

Program Cosinus_Vs_TaylorExpansion(Input,Output);

  (*Programmer:Alireza Mahallati Programmer S-T,Number:8811021 Date:7,9,1388

    This program will input a degree and will calculate cosinus(for radians)

    with taylor expansion and will compare the result with the Cosinus

    Function which has been written for Pascal*)

  Uses CRT;

  Var

    Difference,CosinusFunction,Taylor,Degree,Radians,Part:Real;

    Denominator,Sign,Counter,Sentences:longint;

Begin

  CLRSCR;

  Textcolor(Yellow);

  Writeln('Which degree You want to calculate Cosinus for?');

  Readln(Degree);

  Writeln('How many sentences of Taylor expansion you want to involve?');

  Readln(Sentences);

  Radians:=(4*ArcTan(1))*(Degree)/180;

  Denominator:=1;

  If Sentences=1 Then

    Begin

      Writeln('according to Taylor expa`,Cos( ',Radians:16:14,') is -> 1');

      Readln;

      Halt;

    End

  Else

  Part:=1;

  Taylor:=1;

  Sign:=(-1);

  For Counter:=2 To Sentences Do

    Begin

      Denominator:=((2*Counter)-3)*((2*Counter)-2)*Denominator;

      Part:=(Radians*Radians)*Part;

      Taylor:=Taylor+((Sign)*(Part))/Denominator;

      Sign:=Sign*(-1);

    End;

  CosinusFunction:=Cos(Radians);

  Writeln('----------------');

  Textcolor(Green);

  Writeln;

  Writeln('Cosinus of ',Radians:6:4,' Radians is -> ',Taylor:16:14);

  Writeln;

  Writeln('Cosinus of ',Radians:6:4,' Radians by Cosinus Function is -> '

  ,CosinusFunction:16:14);

  Difference:=ABS(CosinusFunction-Taylor);

  Writeln;

  TextColor(Brown);

  Writeln('Error of Taylor expansion in calculating Cosinus of ',Radians:6:4,' Radians is '

  ,Difference:16:14);

  Writeln;

  Textcolor(White);

  Delay(1500);

  Writeln('CODED BY ALIREZA_M');

  Repeat

    Begin

      Delay(100);

    End;

  Until Keypressed;

End.

***drdebcol*** · 12-31-2009, 08:58 AM

Very good and mathematically correct. For this you need to know maths too !