Решебник по алгебре и начала математического анализа 11 класс Колягин Задание 85

\[\lbrack 0;\ 3\pi\rbrack.\]

\[1)\ tg\ x \geq 3\]

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

\[Ответ:\ \ \]

\[arctg\ 3 \leq x < \frac{\pi}{2};\text{\ \ \ }\]

\[arctg\ 3 + \pi \leq x < \frac{3\pi}{2};\ \]

\[arctg\ 3 + 2\pi \leq x < \frac{5\pi}{2}.\]

\[2)\ tg\ x < 4\]

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

\[Ответ:\ \ \]

\[0 \leq x < arctg\ 4;\text{\ \ \ }\]

\[\frac{\pi}{2} < x < arctg\ 4 + \pi;\text{\ \ }\]

\[\ \frac{3\pi}{2} < x < arctg\ 4 + 2\pi;\text{\ \ \ }\]

\[\frac{5\pi}{2} < x \leq 3\pi.\]

\[3)\ tg\ x \leq - 4\]

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

\[Ответ:\ \ \]

\[\frac{\pi}{2} < x \leq - arctg\ 4 + \pi;\text{\ \ \ }\]

\[\frac{3\pi}{2} < x \leq - arctg\ 4 + 2\pi;\]

\[\ \frac{5\pi}{2} < x \leq - arctg\ 4 + 3\pi.\]

\[4)\ tg\ x > - 3\]

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

\[Ответ:\ \ 0 \leq x < \frac{\pi}{2};\text{\ \ \ }\]

\[- arctg\ 3 + \pi < x < \frac{3\pi}{2};\text{\ \ \ }\]

\[- arctg\ 3 + 2\pi < x < \frac{5\pi}{2};\text{\ \ }\]

\[- arctg\ 3 + 3\pi < x \leq 3\pi.\]