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.

That's because sin and cos are cyclic functions, they do not have either a horizontal nor a vertical asymptote, they keep variating from y=1 to y=-1 all the way.
And easy way to think is picturing a trig circle and realising that as we keep increasing the angle, the value of sin or cosine varies in a closed interval of values (-1,1) 
