(12) If for all positive real numbers $x, y$, the inequality $\frac{y}{4}-\cos ^{2} x \geqslant a \sin x- \frac{9}{y}$ holds, then the range of the real number $a$ is $\qquad$.
(12) $[-3,3]$ Hint: According to the problem, $\cos ^{2} x+a \sin x \leqslant \frac{y}{4}+\frac{9}{y}$ holds for all positive real numbers $x, y$, then the left side must be less than or equal to the minimum value 3 of the right side. Let $t=\sin x$, then
$$
-t^{2}+a t \leqslant 2, t \in[-1,1] \text {. }
$$

Taking $t=-1$, we get $a \geqslant-3$; taking $t=1$, we get $a \leqslant 3$. Moreover, when $a \in[-3,3]$, it is easy to prove that $-t^{2}+a t \leqslant 2$ holds for any $t \in[-1,1]$. Therefore, the range of $a$ is $[-3,3]$.