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Ah! Found it in one of my yellowed notebooks...
sin x = x - (x^3 / 3!) + (x^5 / 5!) - (x^7 / 7!) + (x^9 / 9!) ...
where ^ is "raised to the power of", ie. x^3 = x*x*x
and ! is factorial, ie. 4!=1*2*3*4
Didn't find the asm for it, though. IIRC the angle x was in radians as a signed 16-bit integer and I swapped it down for each "power" except last, and then I had a simple list of precalced factorials longwords, shifted to keep the accumulated sum of quotients within longword bounds.
The result was a signed integer where "1" was $7fffffff, and I think you got one "bit" of result precision for two iterations, so 32 iterations should give 16 bits precision, i.e. 4-5 decimal places.
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