Решебник по алгебре и начала математического анализа 11 класс Алимов Задание 648

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

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

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

\[Ответ:\ \ \]

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

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

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

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

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

\[Ответ:\ \ \]

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

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

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

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

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

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

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

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

\[Ответ:\ \]

\[- \frac{5\pi}{6} + 2\pi n < x < \frac{5\pi}{6} + 2\pi n.\]

\[4)\cos x \leq - \frac{\sqrt{2}}{2}\ \]

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

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

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

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

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

\[Ответ:\ \ \]

\[\frac{3\pi}{4} + 2\pi n \leq x \leq \frac{5\pi}{4} + 2\pi n.\]