Is $\sin(x)$ in $\mathcal{O}(1)$?

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Well I was learning about big-$\mathcal{O}$ notation and I wondered whether $\sin(x)$ is in $\mathcal{O}(1)$.

A function $f(x)$ is in $\mathcal{O}(g(x))$ if $f(x)≤C·g(x)$ for all $x>k$ where $C$ and $k$ are an arbitrary constants. Since $\sin(x)$ has a fixed amplitude, there will always be constant values which we can choose such that $\sin(x)<C$.

So I think that $\sin(x)$ is $\mathcal{O}(1)$.

However, I could not find much information about this on the Internet and Chat GPT says I am wrong.