Games that needed trig in the 90's often used SIN/COS lookup-tables. To keep memory down:

1) you only need the first 1/4 of the Sine table since the remaining 3/4 are either the first 1/4 in reverse and/or with the sign flipped.

2) and of course Sine can also be used as a Cosine lookup if you add pi/2 radians to the cosine angle (wrapping around of course).

3) to avoid the size needed for a table of floats you can of course use integers (scaled by some factor) or fixed-point values.

4) and simple interpolation would get you seemingly more precision.

(Combining all the above was a bit gross so documentation and a good SPI helped.)