Trigonometric tables

Modern computers and pocket calculators now generate trigonometric function values on demand, using special libraries of mathematical code.

Interpolation of simple look-up tables of trigonometric functions is still used in computer graphics, where only modest accuracy may be required and speed is often paramount.

Significant research has been devoted to finding accurate, stable recurrence schemes in order to preserve the accuracy of the FFT (which is very sensitive to trigonometric errors).

A trigonometry table is essentially a reference chart that presents the values of sine, cosine, tangent, and other trigonometric functions for various angles.

[1] Modern computers and calculators use a variety of techniques to provide trigonometric function values on demand for arbitrary angles (Kantabutra, 1996).

In modern form, the identities he derived are stated as follows (with signs determined by the quadrant in which x lies): These were used to construct Ptolemy's table of chords, which was applied to astronomical problems.

These two starting trigonometric values are usually computed using existing library functions (but could also be found e.g. by employing Newton's method in the complex plane to solve for the primitive root of zN − 1).

A significant improvement is to use the following modification to the above, a trick (due to Singleton[2]) often used to generate trigonometric values for FFT implementations: where α = 2 sin2(π/N) and β = sin(2π/N).