$9.2953 \cos ^{2} x \cdot \sin x-\sin ^{3} x<\frac{1}{2}$.
Solution. $\sin x \cdot\left(3 \cos ^{2} x-\sin ^{2} x\right)<\frac{1}{2} \Leftrightarrow \sin x \cdot\left(3-4 \sin ^{2} x\right)<\frac{1}{2} \Leftrightarrow \sin 3 x<\frac{1}{2} \Leftrightarrow$ $\Leftrightarrow-\frac{7 \pi}{6}+2 \pi n<3 x<\frac{\pi}{6}+2 \pi n \Leftrightarrow-\frac{7 \pi}{18}+\frac{2 \pi n}{3}<x<\frac{\pi}{18}+\frac{2 \pi n}{3}$.

Answer: $x \in\left(\frac{\pi}{18}(12 n-7) ; \frac{\pi}{18}(12 n+1)\right)$.