Решебник по алгебре и начала математического анализа 10 класс Колягин Задание 1152

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\[\cos{2x} = - \frac{1}{2}\]

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

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

\[= \pm \frac{2\pi}{3} + 2\pi n\]

\[x = \frac{1}{2} \bullet \left( \pm \frac{2\pi}{3} + 2\pi n \right)\]

\[x = \pm \frac{\pi}{3} + \pi n.\]

\[\ \left\lbrack - \frac{\pi}{2};\ \frac{5\pi}{2} \right\rbrack:\]

\[x_{1} = - \frac{\pi}{3};\]

\[x_{2} = \frac{\pi}{3};\]

\[x_{3} = - \frac{\pi}{3} + \pi = \frac{2\pi}{3};\]

\[x_{4} = \frac{\pi}{3} + \pi = \frac{4\pi}{3};\]

\[x_{5} = - \frac{\pi}{3} + 2\pi = \frac{5\pi}{3};\]

\[x_{6} = \frac{\pi}{3} + 2\pi = \frac{7\pi}{3}.\]