Entwicklung der Sinus-Funktion in einer Taylor-Reihe

[fh_beng]

vielen vielen Dank, das Problem mit der "power" Funktion habe ich nun beheben können. (das hätte auch unser Prof. auch wirklich sagen können )


Bis jetzt habe ich nur das hier erstellen können...

Delphi-Quellcode:

unit Unit1;

interface

uses
  Windows, Messages, SysUtils, Variants, Classes, Graphics, Controls, Forms,
  Dialogs, StdCtrls, math, ExtCtrls;

type
  TForm1 = class(TForm)
    Button1: TButton;
    Image1: TImage;
    Button2: TButton;
    memo1: TMemo;
    procedure Button1Click(Sender: TObject);
    procedure Button2Click(Sender: TObject);
  private
    { Private-Deklarationen }
    function my_fakultaet(n:integer):real;
    function my_pow(x:real;n:integer):real;
    function my_exp(x:real):real;
    function my_ln (x:real):real;
    function my_rpow(x,y:real):real;
    function my_root(x:real;n:integer):real;
    function my_pi:real;
    function my_sin_rad(x:real):real;
    function my_sin_grad(x:real):real;
  public
    { Public-Deklarationen }
  end;

var
  Form1: TForm1;
  steps:integer=10;

implementation

{$R *.dfm}

function Tform1.my_fakultaet(n:integer):real;
Var i:Integer; s:real;
  Begin
    s:=1;
    for i:=1 to n do s:=s*i;
    result:=s;
  End;

function Tform1.my_pow(x:real;n:integer):real;
Var i:integer; s,ds:real;
  Begin
    s:=1;
    if n>0 then for i:=1 to n do s:=s*x;
    result:=s;
  End;

function Tform1.my_exp(x:real):real;
Var i:integer; s,ds,fak:real;
  Begin
    s:=1; fak:=1;
    for i:=1 to steps do
    begin
      fak:=fak*i;
      ds:=my_pow(x,i)/fak;
      s:=s+ds;
    end;
    my_exp:=s;
  End;

function Tform1.my_ln (x:real):real;
Var i,n:integer; s,ds:real;
  Begin
  s:=0;
  for i:=1 to steps do
    begin
      n:=2*i-1;
      ds:=(x-1)/(x+1);
      ds:=my_pow(ds,n)*1/n;
      s:=s+ds;
    end;
    my_ln:=s*2;

  End;

function Tform1.my_rpow(x,y:real):real;
Var i:integer; s,ds:real;
  Begin
    my_rpow:=my_exp(my_ln(x)*y);
  End;

function Tform1.my_root(x:real;n:integer):real;
Var i:integer;
  Begin
    my_root:=my_exp(my_ln(x)/n);
  End;

function Tform1.my_pi :real;
Var i:integer; s,ds:real;
  Begin
    s:=1;
    for i:=1 to steps do
      begin
        ds:=power(-1,i)/((2*i+1)* power(3,i));
        s:=s+ds;
      end;
      my_pi:=6/sqrt(3)*s;

  End;

function Tform1.my_sin_rad(x:real):real;
Var i,j:integer; s,ds:real;
  Begin
    s:=x;
    for i:=1 to steps do
    begin
      j:=2*i+1;
      ds:=power(-1,i)*power(x,j)/my_fakultaet(j);
      s:=s+ds;
    end;
    my_sin_rad:=s;
  End;

function Tform1.my_sin_grad(x:real):real;
Var i:integer;
  Begin
    my_sin_grad:=my_sin_rad(x*my_pi/180);
  End;


procedure TForm1.Button1Click(Sender: TObject);
Var grad,rad,s,ds:real;
    x,xm,y,
      i,
      h,
      xoffset,
      yoffset,
      ix,
      iy,
      endwert
                :integer;
      kopfstand :boolean;

      deltay,
      ydiffz,
      ymin,
      ymax,
      omega,
      sy,
      t
                :double;

begin
   grad:=rad*(180/pi);
   image1.picture:=nil;
   x:=0;
   y:=image1.Height div 2;
   xm:=image1.width;
   image1.Canvas.moveto(x,y);
   image1.canvas.lineto(xm,y);



  begin
  kopfstand:=true;
  omega:=2;
  h:=image1.Height;
  ymin:=-1.1;
  ymax:=1.1;
  ydiffz:=ymax-ymin;
  deltay:=ydiffz/h;
  xoffset:=10;
  yoffset:=h div 2;

  with image1.Canvas do
    begin
    moveto(x,0);
    lineto(x,h);
    moveto(x,y);
    lineto(image1.width,y);
    pen.color:=clblack;
  end;

  Endwert:=trunc(2*pi/0.02/omega);
  for i:=0 to endwert do
    begin
    t:=i*0.02;
    sy:=sin(omega*t);
    x:=i;
    y:=trunc(sy/deltay);
    ix:=trunc(x+xoffset);
    with image1.canvas do
      begin
      if kopfstand then
        begin
        y:=h-y;
        iy:=trunc(y-yoffset)
      end
      else iy:=trunc(y+yoffset);
      if i=0 then
            moveto(ix,iy)
          else
            lineto(ix,iy);
      end;
  end;
end;

end;

procedure TForm1.Button2Click(Sender: TObject);
  begin
  image1.Picture:=nil;
  end;

end.