Modern computers and pocket calculators now generate trigonometric function values on demand, using special libraries of mathematical code. Often, these libraries use precalculated tables internally, and compute the required value by using an appropriate interpolation method.
Simple lookup tables of trigonometric functions are now mostly used in computer graphics, where accurate calculations are either not needed, or cannot be made fast enough.
A quick, but inaccurate approximation
A quick, but inaccurate, algorithm for calculating a table of N approximations a[n] for sin(2πn/N) and b[n] for cos(2πn/N) is:
Unfortunately, this is not a useful algorithm for generating sine tables, for a number of reasons. It will only work as the number of divisions tends towards infinity, with infiniteprecision arithmetic.
For instance, with tablesize N=256, the last sinevalue is computed to be 0.02438606 instead of 0, and N=1024 gives 0.006124031.
If the sine and cosine values obtained were to be plotted, this algorithm would draw a logarithmic spiral rather than a circle.
Calculating accurate approximations for trigonometric functions
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