Решебник по алгебре и начала математического анализа 11 класс Алимов Задание 728

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\[1)\sin{2x} \geq - \frac{1}{2}\]

\[\arcsin\left( - \frac{1}{2} \right) + 2\pi n \leq 2x \leq\]

\[\leq \pi - \arcsin\left( - \frac{1}{2} \right) + 2\pi n\]

\[- \arcsin\frac{1}{2} + 2\pi n \leq 2x \leq\]

\[\leq \pi + \arcsin\frac{1}{2} + 2\pi n\]

\[- \frac{\pi}{6} + 2\pi n \leq 2x \leq \pi + \frac{\pi}{6} + 2\pi n\]

\[- \frac{\pi}{6} + 2\pi n \leq 2x \leq \frac{7\pi}{6} + 2\pi n\]

\[- \frac{\pi}{12} + \pi n \leq x \leq \frac{7\pi}{12} + \pi n\]

\[\left\lbrack - \frac{3\pi}{2};\ \pi \right\rbrack:\]

\[- \frac{3\pi}{2} \leq x_{1} \leq - \frac{17\pi}{12};\]

\[- \frac{13\pi}{12} \leq x_{2} \leq - \frac{5\pi}{12};\]

\[- \frac{\pi}{12} \leq x_{3} \leq \frac{7\pi}{12};\]

\[\frac{11\pi}{12} \leq x_{4} \leq \pi.\]

\[2)\sin{3x} < \frac{\sqrt{3}}{2}\]

\[- \pi - \arcsin\frac{\sqrt{3}}{2} + 2\pi n < 3x <\]

\[< \arcsin\frac{\sqrt{3}}{2} + 2\pi n\]

\[- \pi - \frac{\pi}{3} + 2\pi n < 3x < \frac{\pi}{3} + 2\pi n\]

\[- \frac{4\pi}{3} + 2\pi n < 3x < \frac{\pi}{3} + 2\pi n\]

\[- \frac{4\pi}{9} + \frac{2\pi n}{3} < x < \frac{\pi}{9} + \frac{2\pi n}{3}\]

\[\left\lbrack - \frac{3\pi}{2};\ \pi \right\rbrack:\]

\[- \frac{3\pi}{2} \leq x_{1} < - \frac{11\pi}{9};\]

\[- \frac{10\pi}{9} < x_{2} < - \frac{5\pi}{9};\]

\[- \frac{4\pi}{9} < x_{3} < \frac{\pi}{9};\]

\[\frac{2\pi}{9} < x_{4} < \frac{7\pi}{9};\]

\[\frac{8\pi}{9} < x_{5} \leq \pi.\]