Exact Values of cos(2*k*pi/13)

by Literka


Rozmiar: 871 bajtów

It was shown on the page of Literka Polynomials that the values cos(2*pi/13), cos(4*pi/13), cos(6*pi/13), cos(8*pi/13), cos(10*pi/13), cos(12pi/13) are roots of the polynomial P(x) equal

Rozmiar: 5624 bajtów


Polynomial P(x) is a product of two polynomials Q(x) and R(x)

P(x)=Q(x)*R(x)


where polynomial Q(x) is equal



and polynomial R(x) is equal



Using formulas of the page of Literka cubic formulas we can find roots of polynomials Q(x) and R(x). We receive:



Value of cos(2*pi/13) is equal






Value of cos(4*pi/13) is equal



Value of cos(6*pi/13) is equal






Value of cos(8*pi/13) is equal



Value of cos(10*pi/13) is equal






Value of cos(12*pi/13) is equal






See a similar page about
values of cos(2*k*pi/7).

Exact values of cos(2*k*pi/17).





See the list and descriptions of mathematical pages from Mathematical Countryside.


See other pages of 'Literka' from Mathematical Countryside:
Monotonic subsequences.
A remarkable monotonic property of the gamma function .
An elementary problem can be unsolvable.
Positive random walks.
Weierstrass Approximation Theorem. Bernstein's Polynomials.
Construction of a regular pentagon.
Roots of cubic equation. Cardano's formula.
Roots of quartic equation. Cardano's formula.
Rudin's Theorem of Complex Analysis.
Exact values of trigonometric functions of angles (n*pi)/7.
Exact values of trigonometric functions of angles (n*pi)/11.
Exact values of cos(k*pi)/17.
Exact values of trigonometric functions of angles (n*pi)/17.
Equalities for values of trigonometric functions of angles (n*pi)/17.
Factorization of a polynomial, which defines values of sine function (angles n*pi/17).
Polynomials with roots cos(2*k*pi/n).
Factorization of polynomials with roots cos(2*k*pi/n), where n is Fermat number.
Values of trigonometric functions of angles (n*pi)/257. Part I.
Values of trigonometric functions of angles (n*pi)/257. Part II, Part III, Part IV, Part V, Part VI, Part VII.
Values of trigonometric functions of angles (n*pi)/65537. Part I.
Values of trigonometric functions of angles (n*pi)/65537. Part II, Part III, Part IV and Part V, Part VI, Part VII, Part VIII, Part IX, Part X, Part XI, Part XII, Part XIII, Part XIV.

Construction of a regular heptadecagon.
Construction of a regular polygon with 257 sides.

Software that you really need.

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