Решебник по алгебре и начала математического анализа 11 класс Алимов Задание 713

\[\boxed{\mathbf{713}\mathbf{.}}\]

\[1)\cos x \geq \frac{1}{2}\]

\[- \arccos\frac{1}{2} + 2\pi n \leq x \leq \arccos\frac{1}{2} + 2\pi n\]

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

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

\[0 \leq x_{1} \leq \frac{\pi}{3};\]

\[\frac{5\pi}{3} \leq x_{2} \leq \frac{7\pi}{3}.\]

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

\[- \arccos\left( - \frac{1}{2} \right) + 2\pi n \leq x \leq\]

\[\leq \arccos\left( - \frac{1}{2} \right) + 2\pi n\]

\[- \left( \pi - \arccos\frac{1}{2} \right) + 2\pi n \leq x \leq\]

\[\leq \pi - \arccos\frac{1}{2} + 2\pi n\]

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

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

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

\[0 \leq x_{1} \leq \frac{2\pi}{3};\]

\[\frac{4\pi}{3} \leq x_{2} \leq \frac{8\pi}{3}.\]

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

\[\arccos\left( - \frac{\sqrt{2}}{2} \right) + 2\pi n < x <\]

\[< 2\pi - \arccos\left( - \frac{\sqrt{2}}{2} \right) + 2\pi n\]

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

\[< 2\pi - \left( \pi - \arccos\frac{\sqrt{2}}{2} \right) + 2\pi n\]

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

\[\frac{3\pi}{4} + 2\pi n < x < \frac{5\pi}{4} + 2\pi n;\]

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

\[\frac{3\pi}{4} < x_{1} < \frac{5\pi}{4};\]

\[\frac{11\pi}{4} < x_{2} \leq 3\pi.\]

\[4)\cos x < \frac{\sqrt{3}}{2}\]

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

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

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

\[\frac{\pi}{6} + 2\pi n < x < \frac{11\pi}{6} + 2\pi n;\]

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

\[\frac{\pi}{6} < x_{1} < \frac{11\pi}{6};\]

\[\frac{13\pi}{6} < x_{2} \leq 3\pi.\]