I have observed that the expression $$\frac{\sin(\pi f_n t)}{f_n \sin(\pi t)}.\Pi(t)\approx\text{sinc}(\pi f_n t).\Pi(t)$$ as $f_n$ becomes large and $\Pi(t)$ is the rect($t$) function.
Without the $\Pi(t)$, the left hand term is periodic so the effect of $t$ in the denominator is limited when compared to a sinc() function. However I struggle to see how $f_n$ in concert with sin($\pi t$) drives the observed behaviour.
Would appreciate any insights on this.