Question

Решите неравенство sin x > или равно минус 1/2

Answer 1

$\sin x\geq -\frac12;\\ \sin x=-\frac12;\\ x=-(-1)^n\frac\pi6+\pi n;\\ 1) x\in(-\frac\pi6+2\pi n; \frac{7\pi}{6}+2\pi n):\\ x=\pi n, \sin\pi n=0-\frac12;\\ 2)x\in(\frac{7\pi}{6}+2\pi n; \frac{11\pi}{6}+2\pi n):\\ x=\frac{3\pi}{2}+2\pi n=\sin(\frac{3\pi}{2}+2\pi n)=-1<-\frac12;\\ \\ \\ \\ \\ x\in\left[-\frac\pi6+2\pi n;\ \frac{7\pi}{6}+2\pi n\right], \ \ n\in Z.$