Решебник по алгебре и начала математического анализа 11 класс Колягин Задание 132

\[1)\sin x \geq \cos x\]

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

\[tg\ x \geq 1\]

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

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

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

\[tg\ x \leq 1;\]

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

\[\frac{\pi}{2} + 2\pi n \leq x \leq \frac{5\pi}{4} + 2\pi n.\]

\[Ответ:\ \ \left\lbrack \frac{\pi}{4} + 2\pi n;\ \frac{5\pi}{4} + 2\pi n \right\rbrack.\]

\[2)\ tg\ x > \sin x\]

\[2\pi n < x < \pi + 2\pi n:\]

\[\frac{1}{\cos x} > 0;\ \ \cos x > 0;\]

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

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

\[- \pi + 2\pi n < x < 2\pi n:\]

\[\frac{1}{\cos x} < 0;\ \ \ \cos x < 0;\]

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

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

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