Back in the early 80's a common thing to do in games on 8 bit computers was to implement sin and cos as lookup tables with the angles being 0-255 or 0-128 or something like that and the result also an integer that was some fixed point representation, so you'd do something like:

  vx = (cos[angle] * speed) >> 8;
  vy = (sin[angle] * speed) >> 8;