[dr. F.I.N.]

Код:

function UserFunc(angle: real; count: integer): real;
var
  i: Integer;
begin
  Result := sin(angle);
  for i := 2 to count do
  Result := sin(Result);
end;

function RecursionFunc(angle: real; count: integer): real;
begin
  if count = 1 then Result := sin(angle)
  else
  Result := sin(RecursionFunc(angle, count - 1));
end;

procedure RecursionProc(angle: real; count: integer; var R: real);
begin
  if count = 1 then R := sin(angle)
  else
  RecursionProc(angle, count - 1, R);
end;

Не тестил. Вроде не ошибся