Решебник по алгебре и начала математического анализа 11 класс Колягин Задание 930

\[1)\cos( - 3x) \geq \frac{\sqrt{3}}{2}\]

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

\[- \frac{5\pi}{6} + 2\pi n \leq - 3x \leq \frac{5\pi}{6} + 2\pi n\]

\[- \frac{5\pi}{18} + \frac{2\pi n}{3} \leq x \leq \frac{5\pi}{18} + \frac{2\pi n}{3}.\]

\[Ответ:\ \ \]

\[x \in \left\lbrack - \frac{\pi}{18} + \frac{2\pi n}{3};\ \frac{\pi}{18} + \frac{2\pi n}{3} \right\rbrack.\]

\[2)\cos\left( 2x - \frac{\pi}{3} \right) < - \frac{1}{2}\]

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

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

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

\[\frac{\pi}{2} + \pi n < x < \frac{5\pi}{6} + \pi n.\]

\[Ответ:\ \ x \in \left( \frac{\pi}{2} + \pi n;\ \frac{5\pi}{6} + \pi n \right).\]