Question

sin x/2 cos x/2>-1/4

Answer 1

$\sin \frac{x}{2} \cos \frac{x}{2} \ \textgreater \ - \frac{1}{4} \\ 2\sin \frac{x}{2} \cos \frac{x}{2} \ \textgreater \ - \frac{1}{2} \\ \sin x \ \textgreater \ -0,5 \\ - \frac{\pi}{6} + 2\pi n \ \textless \ x\ \textless \ \frac{7\pi}{6} +2\pi n, n \in Z \\ x \in (- \frac{\pi}{6} + 2\pi n; \frac{7\pi}{6} +2\pi n), n \in Z$