Values of Trigonometric Functions of Angles (n*pi)/65567. Part IV.

				Values of Trigonometric Functions of Angles (n*pi)/65537. Part IV. by 'Literka'.

In the following text we'll be using the notations pi=3.14159... and w=(2*pi)/65537.

We'll be using all notations from the previous pages of Literka Values of trigonometric functions. Part 65537-1, Part 65537-2 and Part 65537-3.
Let us define new subsets B7, B8, B9, B10, B11, B12, B13, B14. For i between 7 and 14 we define subset Bi the following way:

Take the set X equal to A for i=7, equal to B for i=8 and equal to for other i.
We define the set Y of indices the following way: Take a positive number j less or equal to 32768, let j-1=16*u+v with v less than 16.
Assume first that v is less than 8. Then j is an element of Y, if and only if (A with index j) is included in X.
Assume that v is bigger or equal to 8. Then j is an element of Y, if and only if (A with index j) is not included in X.

We define

Take the numbers ti associated with Bi according to the page Part 65537-3.
Using arguments that we used many times, we can derive the formulas: Rozmiar: 48791 bajtów

Rozmiar: 48791 bajtów

We can create now quadratic equations, the way we were doing it before, with roots si and ti. We'll write formulas for roots, but before we introduce new notations:

Notation	Value

Now we can write Rozmiar: 10684 bajtów

Formulas are becoming complicated and new ideas are needed to write them.

See the next parts of this page Part 65537-5, Part 65537-6, Part 65537-7, Part 65537-8, Part 65537-9, Part 65537-10, Part 65537-11, Part 65537-12, Part 65537-13, Part 65537-14.

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 .
Weight centers of simple geometrical figures.
An elementary problem can be unsolvable.
Rudin's Theorem of Complex Analysis.
Construction of a regular pentagon.
Construction of a regular heptadecagon.
Construction of a regular polygon with 257 sides.
Roots of cubic equation. Cardano's formula.
Weierstrass Approximation Theorem.
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.
Values of trigonometric functions of angles (n*pi)/257. Part III.
Values of trigonometric functions of angles (n*pi)/257. Part IV.
Values of trigonometric functions of angles (n*pi)/257. Part V.
Values of trigonometric functions of angles (n*pi)/257. Part VI.
Values of trigonometric functions of angles (n*pi)/257. Part VII.

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