We know that for any integer $n$, $\sin(n)$ can never equal to one. So what is the maximum value of $sin(n)$? How close can the sine of an integer get to unity?
I'll be really interested to know if such a value exists.
2026-04-08 17:46:24.1775670384
Maximum value of $\sin(n)$ for integer $n$
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It doesn't exist. It can be proved that $\sup\{\sin n\,|\,n\in\mathbb{Z}\}=1$, but, as you wrote, $\sin(n)$ is never $1$, if $n\in\mathbb Z$.