I don't know how computers compute trig functions but I think I thought of a very fast way to do it.

First there's half angle identities but I'd like to divide an angle by 5 then bisect that angle. Now you have 1/10th angle identities and I'd like to do it again to get 1/100th angle identities and so on for each decimal place. Then all you have to do is use each identity for each decimal digit of the angle.

So for every pixel of a 3 dimensional environment computers have to use sine, cosine and tangent. Making it as fast as possible would be a must.

So does anyone know how to algebraically trisect an angle? For 1/4th it would be 2 half angle identities however 1/5th would be the big one.