= Solution
For $x>0$, the denominator is positive, so the <function graph> has the same sign as $\sin x$. Its crossings of the horizontal axis are
$$
\boxed{x=n\pi,\qquad n=1,2,3,\ldots.}
$$
Each crossing is genuine because the <derivative> there is $(-1)^n/(n\pi)^2\ne0$. Near zero, $\sin x\sim x$, so $y\sim1/x\to+\infty$; the origin is excluded and is not a crossing. The oscillations alternate sign and decay towards zero as $x\to\infty$, with <absolute value> at most $1/x^2$.
\Image[/past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2022/paper-1-q7-oscillation.png]
{title=The positive-axis graph in Question 7, with its crossings at positive integer multiples of $\pi$}
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