Values of Trigonometric Functions of Angles (n*pi)/65537. Part V.

				Values of Trigonometric Functions of Angles (n*pi)/65537. Part V. 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, Part 65537-3. and Part 65537-4.
Let us define new subset B15, B16, B17, B18, ... B29, B30. For i between 16 and 30 we define subset Bi the following way:

Take the set X equal to A for i=15, equal to B for i=16 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=32*u+v with v less than 32.
Assume first that v is less than 16. 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 16. Then j is an element of Y, if and only if (A with index j) is not included in X.

From now we'll be using the following notation:

Then

Values of hi are shown on the applet below. Formulas above show how in a simple way find ti knowing hi. Signs plus or minus in the formula for ti can be determined in a different way. In our case the sequence of signs looks like this: "+-+++--+-+-+-+--". Values hi were computed in a usual way as on previous pages.
You can see formulas for hi clicking on orange area and the same to return.

Now we know 32 values of ti (or si). We need to know 2048. So, still there is a long way ahead.

See the next parts of this page 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.

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