Решебник по алгебре и начала математического анализа 11 класс Алимов Задание 653

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\[1)\cos{\left( \frac{x}{3} + 2 \right) \geq \frac{1}{2}}\]

\[- \arccos\frac{1}{2} + 2\pi n \leq \frac{x}{3} + 2\]

\[\frac{x}{3} + 2 \leq \arccos\frac{1}{2} + 2\pi n\]

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

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

\[Ответ:\ \]

\[- \pi - 6 + 6\pi n \leq x \leq \pi - 6 + 6\pi n.\]

\[2)\sin\left( \frac{x}{4} - 3 \right) < - \frac{\sqrt{2}}{2}\]

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

\[< \frac{x}{4} - 3 < \arcsin\left( - \frac{\sqrt{2}}{2} \right) + 2\pi n\]

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

\[< \frac{x}{4} - 3 < - \arcsin\frac{\sqrt{2}}{2} + 2\pi n\]

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

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

\[- \frac{3\pi}{4} + 3 + 2\pi n < \frac{x}{4} < - \frac{\pi}{4} + 3 + 2\pi n.\]

\[Ответ:\ \]

\[- 3\pi + 12 + 8\pi n < x < - \pi + 12 + 8\pi n.\]