[Uniq!]

Код:

function myfact(n: integer): integer;
begin
  if n <= 1 then Result := 1;
  if n > 1 then Result := n * myfact(n - 1);
end;

function myPower(a, b: real): real;
begin
  Result := exp(b * ln(a));
end;

function mycos(c: real; it: integer): real;
var
  i: byte;
begin
  Result := 1;
  for i := 1 to it do
  begin
  if (i mod 2) = 1 then
    Result := Result - (myPower(c, i*2) / myfact(i*2));
  if (i mod 2) = 0 then
    Result := Result + (myPower(c, i*2) / myfact(i*2));
  end;
end;

procedure TForm1.Button1Click(Sender: TObject);
begin
  Label1.Caption := FloatToStr(cos(3.14/2));
  Label2.Caption := FloatToStr(mycos(3.14/2,5));
end;

Некогда объяснять. Писал на коленке. devision by zero ... ожидаемо