Question

2sin (2x - p/3) +1 >= 0

Answer 1

$2\sin(2x - \frac{\pi}{3} ) + 1 \geq 0\\ \sin(2x - \frac{\pi}{3} ) \geq -0,5 \\ \ -\frac{\pi}{6} + 2\pi n \leq 2x - \frac{\pi}{3} \leq \frac{7\pi}{6} + 2\pi n,n \in Z\\ \frac{\pi}{6} + 2\pi n \leq 2x \leq \frac{3\pi}{2} + 2\pi n,n \in Z\\ \frac{\pi}{12} + \pi n \leq x \leq \frac{3\pi}{4} + \pi n,n \in Z \\ x \in [\frac{\pi}{12} + \pi n; \frac{3\pi}{4} + \pi n] , n \in Z$