Calculate function Graphically

private
    { Private declarations }
    procedure CalculateGraph;
    
var
  Form1: TForm1;
  FPoints: array [0..144] of TPoint;
  
//

procedure TForm1.CalculateGraph;
var
  xRangePixels, yRangePixels: Integer;
  origin: TPoint;
  radian, interval: Double;
  i: Integer;
begin
  xRangePixels := (paintbox1.Width - 2) div 4; { pixels in Pi }
  yRangePixels := (paintbox1.Height - 2) div 2; { pixels in 1 }
  origin       := Point(paintbox1.Width div 2, paintbox1.Height div 2);
  radian       := -2.0 * Pi;
  interval     := 4.0 * Pi / 144.0;
  for i := 0 to High(FPoints) do
  begin
    FPoints[i].X := origin.x + Round(radian * xRangePixels / Pi);
    FPoints[i].Y := origin.y - Round(sin(radian) * yRangePixels);
    radian       := radian + interval;
  end;
end;

procedure TForm1.PaintBox1Paint(Sender: TObject);
var
  origin: TPoint;
  xRangePixels, yRangePixels: Integer;
begin
  with PaintBox1.Canvas do 
  begin
    { Fill background in white }
    Brush.Color := clBtnFace;
    Brush.Style := bsSolid;
    Fillrect(paintbox1.BoundsRect);

    { Paint a coordinate cross }
    origin    := Point(paintbox1.Width div 2, paintbox1.Height div 2);
    Pen.Color := clBlack;
    Pen.Style := psSolid;
    Pen.Width := 1;
    MoveTo(1, origin.Y);
    LineTo(paintbox1.Width - 1, origin.y);
    MoveTo(origin.x, 1);
    LineTo(origin.x, paintbox1.Height - 1);

    { Paint some tickmarks and label the axis }
    Font.Name    := 'Symbol';
    Font.Size    := 8;
    Font.Color   := clBlack;
    xRangePixels := (paintbox1.Width - 2) div 4; { pixels in Pi }
    yRangePixels := (paintbox1.Height - 2) div 2; { pixels in 1 }

    { X axis }
    MoveTo(origin.x - 2 * xRangePixels, origin.y - 4);
    LineTo(origin.x - 2 * xRangePixels, origin.y + 4);
    TextOut(origin.x - 2 * xRangePixels + 2, origin.y + 2, '-2p');
    MoveTo(origin.x - xRangePixels, origin.y - 4);
    LineTo(origin.x - xRangePixels, origin.y + 4);
    TextOut(origin.x - xRangePixels + 2, origin.y + 2, '-p');
    MoveTo(origin.x + xRangePixels, origin.y - 4);
    LineTo(origin.x + xRangePixels, origin.y + 4);
    TextOut(origin.x + xRangePixels - 2 - TextWidth('p'), origin.y + 2, 'p');
    MoveTo(origin.x + 2 * xRangePixels, origin.y - 4);
    LineTo(origin.x + 2 * xRangePixels, origin.y + 4);
    TextOut(origin.x + 2 * xRangePixels - 2 - TextWidth('2p'), origin.y + 2, '2p');

    { Y axis }
    MoveTo(origin.x - 4, origin.y - yRangePixels);
    LineTo(origin.x + 4, origin.y - yRangePixels);
    TextOut(origin.x + 4, origin.y - yRangePixels, '1.0');
    MoveTo(origin.x - 4, origin.y - yRangePixels div 2);
    LineTo(origin.x + 4, origin.y - yRangePixels div 2);
    TextOut(origin.x + 4, origin.y - (yRangePixels + TextHeight('1')) div 2, '0.5');
    MoveTo(origin.x - 2, origin.y + yRangePixels div 2);
    LineTo(origin.x + 2, origin.y + yRangePixels div 2);
    TextOut(origin.x + 3, origin.y + (yRangePixels - TextHeight('1')) div 2, '-0.5');
    MoveTo(origin.x - 2, origin.y + yRangePixels);
    LineTo(origin.x + 2, origin.y + yRangePixels);
    TextOut(origin.x + 3, origin.y + yRangePixels - TextHeight('1'), '-1.0');

    {Paint the graph }
    Pen.Color := clBlue;
    Polyline(FPoints);
  end;
end;

procedure TForm1.FormResize(Sender: TObject);
begin
  CalculateGraph;
end;

procedure TForm1.FormCreate(Sender: TObject);
begin
  CalculateGraph;
end;