>>13479491There are various ways.
1. The most obvious one is to solve a cubic equation to get the value of the sine of one degree (as explained in the PDF linked by this Anon
>>13479758) and then use addition formulas.
2. Another method (as mentioned by many Anons in this thread) is to use Taylor's formula, which allows you to get the value of any trigonometric function to any degree of accuracy you want (just use enough terms of the expansion and calculate the error using the remainder of the Taylor's polynomial).
3. Yet another method is the CORDIC algorithm, that uses linear algebra and lookup tables to compute the value of trigonometric functions. This algorithm is the one actually used by most computers and calculators to find the values of trigonometric functions (even if many people tend to believe that Taylor's formula is what calculators use). The caveat is that you do need some values of the arc tangent in order to use this algorithm (those values are stored in the lookup table used by the algorithm), but the values needed are for fairly small angles, and since as x tends to zero we have that [arctan(x)]/x tends to 1, it is possible to use the approximation arctan(x) ? x so that you don't have to get those values of the arctan by some other mean. Once you have those values, the rest is just linear algebra.
