Values of Trigonometric Functions of Angles
(n*pi)/65537. Part II.
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 of the previous part of this page
Values of trigonometric functions.
Part 65537-1.
On this page sets A, B, C were defined and the sums of cosines corresponding to these sets were computed.
On the current page we'll do the same, but for different sets. This will approach us to achieve the final
result.
Let us define set B1 to be the union of the sets Ai (defined before on the quoted page) with indices i,
which qive rests 1 and 2 in a division by 4. Hence, the sequence of indices is 1,2,5,6...2046.
Let us define set C1 to be all other elements of the set A (i.e. it a difference of the sets A and B1).
Finally let
Hence, t1 and s1 are the roots of the quadratic equation:
Solving it and verifying values we receive:
Similarly let us define set B2 to be the union of the sets Ai with indices i giving rests 0 and 1
in a division by 4.
Let C2 be the difference of sets A and B2 and
By the same arguments as before
and
The same way as before we derive formulas of this page:
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