At large times, $\sin(\omega t)$ tends to zero?

While doing a calculation in quantum mechanics, I got a expression $\sin(\omega t)$, and my prof said if I consider the consider at large times, then i can assume that this goes to zero because at large times, the graph of $\sin$ oscillates very rapidly and so you can take it to be zero. When i asked about this he said we want to check for $\frac{\Delta t}{t}$(no units) which should be invariant, and so at large times, we need to take long time(means many cycles) for same ration of $\frac{\Delta t}{t}$.

But I wasn’t convinced by this explanation. I want to know is this mathematically consistent.

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