This small sinus generator is made by KarL/NoooN. It was published in ACE CD #2, and I found it in the PC DEMOS FAQ. I quote from the FAQ, with some estethical modifications:

Here's some explanation about the sinus table generator in the ACE BBS advert. The method used is a recursive sinus sythesis. It's possible to compute all sinus values with only the two previous ones and the value of cos(2ã/N), where n is the number of values for one period. It's as follow:

Sin(K)=2.Cos(2ã/N).Sin(K-1)-Sin(K-2)

or

Cos(K)=2.Cos(2ã/N).Cos(K-1)-Cos(K-2)

The last one is easiest to use, because the two first values of the cos table are 1 and cos(2ã/n) and with this two values you are able to build all the following. Some simple code (the cos table has 1024 values and ranges from -2^24 to 2^24):

build_table:    lea    di,cos_table
                mov    cx,1022
                mov    ebx,cos_table[4]
                mov    eax,ebx
@@calc:
                imul   ebx
                shrd   eax,edx,23
                sub    eax,[di-8]
                stosd
                loop   @@calc

cos_table       dd     16777216         ; 2^24
                dd     16776900         ; 2^24*cos(2ã/1024)
                dd     1022     dup (?)