Решебник по алгебре и начала математического анализа 11 класс Колягин Задание 41

\[- \frac{\pi}{2} \leq x \leq \frac{3\pi}{2}.\]

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

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

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

\[Ответ:\ - \frac{\pi}{2} \leq x < - \frac{\pi}{6};\ \ \ \]

\[\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\frac{\pi}{6} < x < \frac{5\pi}{6};\ \ \ \]

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

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

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

\[- \frac{\pi}{18} + \frac{2\text{πn}}{3} < x < \frac{\pi}{18} + \frac{2\text{πn}}{3}.\]

\[Ответ:\ - \frac{\pi}{18} < x < \frac{\pi}{18};\]

\[\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\frac{11\pi}{18} < x < \frac{13\pi}{18};\]

\[\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\frac{23\pi}{18} < x < \frac{25\pi}{18}.\]