Given the recurrence, $x_k = \sin (x_{k-1})$ where $x_1 \neq 0$, I know that $x_k \rightarrow 0$ as $k \rightarrow \infty$. I am looking for a simple $f(k)$ such that $|x_k| = \Theta(f(k))$. Any ideas on where to start?
2026-04-13 06:16:53.1776061013
Asymptotic behavior of $x_k = \sin (x_{k-1})$
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