Let’s find horizontal asymptotes with help of the limits of this function at x->+oo and x->-oo
$$\lim_{x \to -\infty}\left(\frac{x \sin{\left(1 \right)}}{x}\right) = \sin{\left(1 \right)}$$
Let's take the limitso,
equation of the horizontal asymptote on the left:
$$y = \sin{\left(1 \right)}$$
$$\lim_{x \to \infty}\left(\frac{x \sin{\left(1 \right)}}{x}\right) = \sin{\left(1 \right)}$$
Let's take the limitso,
equation of the horizontal asymptote on the right:
$$y = \sin{\left(1 \right)}$$