I'm doing some exam review and I thought I might need to use something like this. Is it true? If not, is there a similar statement, and if so, how can we prove it? $\sin\left(\frac1{n^k}\right) < \frac1{n^k} \forall n,k\in \mathbb{N}$
I can't find it on the site or in my textbook, but it seems to be an assumption used quite a bit (or some variation of it). I'm assuming if it's true it can be improved to say for all real numbers greater than 1? Or possibly even better?
I tried checking on wolfram, but I'm not sure how to ask a question and make it accept conditions : http://www.wolframalpha.com/input/?i=is+sin%281%2Fn%29+%3C+1%2Fn