I idontknow Dec 2015 930 122 Earth Dec 6, 2019 #1 Express \(\displaystyle \sin(1/n)\) in terms of \(\displaystyle \sin(n) \; \) , where \(\displaystyle n\in \mathbb{N} \).

Express \(\displaystyle \sin(1/n)\) in terms of \(\displaystyle \sin(n) \; \) , where \(\displaystyle n\in \mathbb{N} \).

tahirimanov19 Mar 2015 182 68 Universe 2.71828i3.14159 Dec 6, 2019 #2 Use magic. And where did you get this problem from? Generalize the problem for \(\displaystyle z\), where \(\displaystyle z \in \mathbb{C}\). Reactions: idontknow

Use magic. And where did you get this problem from? Generalize the problem for \(\displaystyle z\), where \(\displaystyle z \in \mathbb{C}\).

I idontknow Dec 2015 930 122 Earth Dec 6, 2019 #3 Let \(\displaystyle \sin(n)=t\) , \(\displaystyle 1/n=1/\arcsin(t)\) , both sides -sin. \(\displaystyle \sin(1/n)=\sin(1/\arcsin(t))\). Can we accept this solution ?

Let \(\displaystyle \sin(n)=t\) , \(\displaystyle 1/n=1/\arcsin(t)\) , both sides -sin. \(\displaystyle \sin(1/n)=\sin(1/\arcsin(t))\). Can we accept this solution ?

tahirimanov19 Mar 2015 182 68 Universe 2.71828i3.14159 Dec 6, 2019 #4 No, your answer should be in terms of \(\displaystyle \sin(n)\), not in terms of \(\displaystyle \sin(arcofnoah(n))\)

No, your answer should be in terms of \(\displaystyle \sin(n)\), not in terms of \(\displaystyle \sin(arcofnoah(n))\)

M mathman Forum Staff May 2007 6,888 759 Dec 6, 2019 #5 Highly unlikely $\lim_{n\to \infty} \sin(1/n)=0$ while $\sin(n)$ does not converge to anything as $n \to \infty$.

Highly unlikely $\lim_{n\to \infty} \sin(1/n)=0$ while $\sin(n)$ does not converge to anything as $n \to \infty$.

romsek Math Team Sep 2015 2,753 1,534 USA Dec 6, 2019 #6 I'm thinking the MacLaurin series should be the first step

V v8archie Math Team Dec 2013 7,709 2,677 Colombia Dec 6, 2019 #7 The question sounds like a Fourier Series question, but since $\sin\frac1n$ isn't periodic, there's a problem. Reactions: idontknow

The question sounds like a Fourier Series question, but since $\sin\frac1n$ isn't periodic, there's a problem.

romsek Math Team Sep 2015 2,753 1,534 USA Dec 6, 2019 #8 yeah wait... do you know if this problem has a solution? Or are you just slinging random ... stuff... out there? Reactions: idontknow

yeah wait... do you know if this problem has a solution? Or are you just slinging random ... stuff... out there?