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Trigonometric functions of pi/p for p prime have an especially complicated Galois-minimal representation. In particular, the case cos(pi/23) requires approximately 500 MB of ...

Rather surprisingly, trigonometric functions of npi/17 for n an integer can be expressed in terms of sums, products, and finite root extractions because 17 is a Fermat prime. ...

The exact values of cos(pi/18) and sin(pi/18) can be given by infinite nested radicals sin(pi/(18))=1/2sqrt(2-sqrt(2+sqrt(2+sqrt(2-...)))), where the sequence of signs +, +, ...

The constant pi, denoted pi, is a real number defined as the ratio of a circle's circumference C to its diameter d=2r, pi = C/d (1) = C/(2r) (2) pi has decimal expansion ...

The angles mpi/n (with m,n integers) for which the trigonometric functions may be expressed in terms of finite root extraction of real numbers are limited to values of m ...

cos(pi/8) = 1/2sqrt(2+sqrt(2)) (1) cos((3pi)/8) = 1/2sqrt(2-sqrt(2)) (2) cot(pi/8) = 1+sqrt(2) (3) cot((3pi)/8) = sqrt(2)-1 (4) csc(pi/8) = sqrt(4+2sqrt(2)) (5) csc((3pi)/8) ...

The study of angles and of the angular relationships of planar and three-dimensional figures is known as trigonometry. The trigonometric functions (also called the circular ...

Trigonometric functions of npi/11 for n an integer cannot be expressed in terms of sums, products, and finite root extractions on real rational numbers because 11 is not a ...

The trigonometric formulas for pi/5 can be derived using the multiple-angle formula sin(5theta)=5sintheta-20sin^3theta+16sin^5theta. (1) Letting theta=pi/5 and x=sintheta ...

Trigonometric functions of npi/9 radians for n an integer not divisible by 3 (e.g., 40 degrees and 80 degrees) cannot be expressed in terms of sums, products, and finite root ...