sine/cosine in fixed_pkg

No. There are no sin or cosine functions available in synthsisable VHDL.

You will need to setup a lookup table of fixed point values but you can use the sin/cosine functions for the real type to set this up. You will need a function to setup your ROM, but this is a great example of a initialisation function:

eg:

type sin_table_t is array(0 to 1023) sfixed(0 downto -15);
function set_sin_table return sin_table_t is
  variable ret_table : sin_table_t;
begin
  for i in 0 to 1023 loop
    ret_table(i) := to_sfixed( (real(i) * MATH_PI) / 1024.0, 0, -15);
  end loop;
  return ret_table;
end function set_sin_table;
--This look up table has 1024 points of sin 0 - PI
constant SIN_TABLE : sin_table_t := set_sin_table;

Then you use the input to the table to be the fraction of pi for the value

output <= SIN_TABLE(X);

X here represents the fraction of PI, so setting X to 500 in real terms means sin(PIx500 / 1024).