Why can't we determine the limit of $\cos x$ and $\sin x$ at $x=\infty $ or $x=-\infty$? I'm confused about why we can't determine the limit of $\cos x$ and $\sin x$ as  $x \to \infty$, even though they are defined over  $\mathbb{R}.$
When I use Wolfram Alpha, I get the following result (link to page):



which shows only that there are $2$ limits :$-1$ and $ 1 $.
Can someone show me why we can't determine $\lim \sin x$ and $\lim \cos x$ at  $x=\infty $ or $x=-\infty$ ?
Thank you for your help.

It does not have two limits. What it says is that it cos or sin is always between -1 and 1 as x tends to infinity. Breaking news...
Actually it has no limit because by definition of the limit of a function f at +infinity, at a certain point A, for every x>=A, f(x) must stay "near" a certain value, and grow nearer and nearer as x increases. It is clearly not the case here, since cos and sin are oscillating continuously.
