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What is the value of $\sin(x)$ if $x$ tends to infinity?

As in wikipedia entry for "Sine", the domain of $\sin$ can be from $-\infty$ to $+\infty$. What is the value of $\sin(\infty)$?

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    It says that the domain is $(-\infty,\infty)$ which means the endpoints $\infty$ and $-\infty$ are not included in the domain. That is, the function $\sin x$ is not defined at those points, $\infty$ and $-\infty$. However we can talk about the limit of this function as it tends to those points, only to be disppointed that the limits don't exist as well!2012-03-04
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    Can you define what is $\infty-1$?2012-03-04
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    $(-\infty,\infty)$ is just another way to express the set of all real numbers.2012-03-04
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    @Kannappan: There's no way to make sense of it as a real number.2012-03-04
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    @Patrick Precisely. I was waiting for OP to realise that!2012-03-04
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    @KannappanSampath: We can make sense of it ($\infty -1$) : http://en.wikipedia.org/wiki/Extended_real_number_line. And a way to make sense of $\sin \infty$ is to take the limit if it exists (as you already stated :-))2012-03-04
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    @Aryabhata Well, sine function is not defined on the extended real line. Even on exteded real line, $\infty-1=\infty$. I mean $\infty$ and $-\infty$ are symbols attached to $\Bbb R$ for some reasons!2012-03-04
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    @KannappanSampath: Yes, just thought that you might be interested in it (if you didn't already know about it). Not disputing the fact that limit of $\sin x$ as $x \to \infty$ does not exist etc.2012-03-04
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    That doesn't matter. The function $x^2/x$ is also not defined in $0$, but the limit is.2012-03-04
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    @Aryabhata Sorry if my comments had come as rude to you. Well, someone could write an answer showing that the limit at infinity does not exist, prove it and whatnot.2012-03-04
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    @KannappanSampath: No, I didn't find it rude. No worries :-)2012-03-04

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