real analysis - 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.