Решебник по алгебре и начала математического анализа 11 класс Алимов Задание 737

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

\[arctg\ 1 + \pi n \leq x < \frac{\pi}{2} + \pi n\]

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

\[( - \pi;\ 2\pi):\]

\[- \frac{3\pi}{4} \leq x_{1} < - \frac{\pi}{2};\]

\[\frac{\pi}{4} \leq x_{2} < \frac{\pi}{2};\]

\[\frac{5\pi}{4} \leq x_{3} < \frac{3\pi}{2}.\]

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

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

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

\[( - \pi;\ 2\pi):\]

\[- \pi < x_{1} < - \frac{5\pi}{6};\]

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

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

\[\frac{3\pi}{2} < x_{4} < 2\pi.\]

\[3)\ tg\ x < - 1\]

\[- \frac{\pi}{2} + \pi n < x < arctg( - 1) + \pi n\]

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

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

\[( - \pi;\ 2\pi):\]

\[- \frac{\pi}{2} < x_{1} < - \frac{\pi}{4};\]

\[\frac{\pi}{2} < x_{2} < \frac{3\pi}{4};\]

\[\frac{3\pi}{2} < x_{3} < \frac{7\pi}{4}.\]

\[4)\ tg\ x \geq - \sqrt{3}\]

\[\text{arctg}\left( - \sqrt{3} \right) + \pi n \leq x < \frac{\pi}{2} + \pi n\]

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

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

\[( - \pi;\ 2\pi):\]

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

\[- \frac{\pi}{3} \leq x_{2} < \frac{\pi}{2};\]

\[\frac{2\pi}{3} \leq x_{3} < \frac{3\pi}{2};\]

\[\frac{5\pi}{3} \leq x_{4} < 2\pi.\]