User talk:Dissipate

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And don't forget, the edit summary is your friend. :) Oleg Alexandrov (talk) 02:10, 15 March 2006 (UTC)

Hello
I've seen your important contributions for the article Recurrence relation. I'm looking for the general (non-iterative) non-trigonometric expression for the exact trigonometric constants of the form: $$\begin{align}\cos \frac{\pi}{2^n}\end{align}$$, when n is natural (and is not given in advance). Do you know of any such general (non-iterative) non-trigonometric expression? (note that any exponential-expression-over-the-imaginaries is also excluded since it's trivially equivalent to a real-trigonometric expression). Eliko (talk) 08:26, 31 March 2008 (UTC)
 * Let me explain: if we choose n=1 then the term $$\begin{align}\cos \frac{\pi}{2^n}\end{align}$$ becomes "0", which is a simple (non-trigonometric) constant. If we choose n=2 then the term $$\begin{align}\cos \frac{\pi}{2^n}\end{align}$$ becomes $$\begin{align}\frac{1}{\sqrt{2}}\end{align}$$, which is again a non-trigonometric expression. etc. etc. Generally, for every natural n, the term $$\begin{align}\cos \frac{\pi}{2^n}\end{align}$$ becomes a non-trigonometric expression. However, when n is not given in advance, then the very expression $$\begin{align}\cos \frac{\pi}{2^n}\end{align}$$ per se - is a trigonometric expression. I'm looking for the general (non-iterative) non-trigonometric expression equivalent to $$\begin{align}\cos \frac{\pi}{2^n}\end{align}$$, when n is not given in advance. If not for the cosine - then for the sine or the tangent or the cotangent.