If it is easier, you can do it the other way around, by writing $\cos(\pi t)$ in terms of $\cos(\frac{\pi t}{2^n})$. I just wanted to know if there was a nice closed form solution to a problem like this, and, if so, how many terms scale up with how large $n$ scales up.
2026-03-29 19:11:55.1774811515
What is $\cos(\frac{\pi t}{2^n})$ in terms of $\cos(\pi t)$?
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Writing $\cos(\pi t)$ in terms of $\cos(\frac{\pi t}{2^n})$ ... the same thing as writing $\cos(2^n\theta)$ in terms of $\cos(\theta)$ ... is a Chebyshev polynomial