-\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;\\
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x\in\left[-\frac\pi6+2\pi n;\ \frac{7\pi}{6}+2\pi n\right], \ \ n\in Z." alt="\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;\\
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x\in\left[-\frac\pi6+2\pi n;\ \frac{7\pi}{6}+2\pi n\right], \ \ n\in Z." align="absmiddle" class="latex-formula">