Trigonacci Grows Up

Most formulas I have developed so far circle around the circular trigonometric functions, sine and cosine.

The dependency is evident. It is time for our trigonacci to come of age and find a representation for itself that does not use sine and cosine, but only the angle “x” and the dimension “n”. This can be done by re-opening our Calculus II book to the chapter on power series. The power series representation of sine and cosine are as follows:

By substituting the trigonometric functions with the power series, we get the following independent trigonacci formulas in the form of a power series. Since the "n" is the same nth term for both the series and the Fibonacci sequence (represented as dimensions in spiral coordinates), and since the limits of the power series coincide with the domain of trigonacci functions, the formula as a whole can be brought under sigma.