Решебник по алгебре и начала математического анализа 11 класс Колягин Задание 88

\[- \frac{\pi}{2} < x < \frac{\pi}{2}.\]

\[1)\ tg\ 2x \leq 1\]

\[- \frac{\pi}{2} + \pi n < 2x \leq \frac{\pi}{4} + \text{πn}\]

\[- \frac{\pi}{4} + \frac{\pi n}{2} < x \leq \frac{\pi}{8} + \frac{\pi n}{2}.\]

\[Ответ:\ - \frac{\pi}{2} < x \leq - \frac{3\pi}{8};\text{\ \ \ }\]

\[- \frac{\pi}{4} < x \leq \frac{\pi}{8};\text{\ \ \ }\frac{\pi}{4} < x < \frac{\pi}{2}.\]

\[2)\ tg\ 3x < - \sqrt{3}\]

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

\[- \frac{\pi}{6} + \frac{\pi n}{3} < x < - \frac{\pi}{9} + \frac{\pi n}{3}.\]

\[Ответ:\ - \frac{\pi}{2} < x < - \frac{4\pi}{9};\]

\[- \frac{\pi}{6} < x < - \frac{\pi}{9};\text{\ \ \ }\frac{\pi}{6} < x < \frac{2\pi}{9}\text{.\ }\]

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

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

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

\[Ответ:\ - \frac{\pi}{2} < x < 0.\]

\[4)\ ctg\frac{x}{3} \geq 1\]

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

\[3\pi n < x \leq \frac{3\pi}{4} + 3\pi n.\]

\[Ответ:\ \ 0 < x < \frac{\pi}{2}.\]