Is $\sin(x) = O(1)$, as $x\to \infty$?

87 Views Asked by At

I read through a lot of literature and it feels like the more I read, the more confused I become. For this question, I argued that as $x$ tends to $\infty$, the value of $\sin(x)$ would oscillate between $-1$ and $1$ only and you cannot fix a specific constant or a function to represent its growth. But some others are saying that since the sine function is bounded between -1 and 1, $| \sin(x) | \le 1$, which is the definition of $O$ notation, it is true. Are there any steps that I can follow to evaluate whether the notation is true or not?