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Trigonometric numbers

Trigonometric numbers are the cosines or sines of angles that are rational multiples of π {\displaystyle \pi }. These numbers are always algebraic, but they may not be constructible. The cosine or sine of the angle 2 π / n {\displaystyle 2\pi /n} is constructible only for certain special numbers n {\displaystyle n}:

Thus, for example, cos (π / 15) {\displaystyle \cos(\pi /15)} is constructible because 15 is the product of the Fermat primes 3 and 5; but cos (π / 9) {\displaystyle \cos(\pi /9)} is not constructible (not being the product of distinct Fermat primes) and neither is cos (π / 7) {\displaystyle \cos(\pi /7)} (being a non-Fermat prime).