Решебник по алгебре и начала математического анализа 11 класс Алимов Задание 716

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\[1)\cos{2x} < \frac{1}{2}\]

\[\arccos\frac{1}{2} + 2\pi n < 2x < 2\pi - \arccos\frac{1}{2} + 2\pi n\]

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

\[\frac{\pi}{3} + 2\pi n < 2x < \frac{5\pi}{3} + 2\pi n\]

\[\frac{\pi}{6} + \pi n < x < \frac{5\pi}{6} + \pi n\]

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

\[- \frac{\pi}{2} \leq x_{1} < - \frac{\pi}{6};\]

\[\frac{\pi}{6} < x_{2} < \frac{5\pi}{6};\]

\[\frac{7\pi}{6} < x_{3} \leq \frac{3\pi}{2}.\]

\[2)\cos{3x} > \frac{\sqrt{3}}{2}\]

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

\[- \frac{\pi}{6} + 2\pi n < 3x < \frac{\pi}{6} + 2\pi n\]

\[- \frac{\pi}{18} + \frac{2\pi n}{3} < x < \frac{\pi}{18} + \frac{2\pi n}{3}\]

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

\[- \frac{\pi}{18} < x_{1} < \frac{\pi}{18};\]

\[\frac{11\pi}{18} < x_{2} < \frac{13\pi}{18};\]

\[\frac{23\pi}{18} < x_{3} < \frac{25\pi}{18}.\]