Решебник по алгебре и начала математического анализа 11 класс Колягин Задание 859

\[\cos\left( 3x - \frac{\pi}{4} \right) = \frac{1}{2}:\]

\[3x - \frac{\pi}{4} = \pm \arccos\frac{1}{2} + 2\pi n =\]

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

\[3x_{1} = - \frac{\pi}{3} + \frac{\pi}{4} + 2\pi n =\]

\[= - \frac{\pi}{12} + 2\pi n;\]

\[3x_{2} = + \frac{\pi}{3} + \frac{\pi}{4} + 2\pi n = \frac{7\pi}{12} + 2\pi n;\]

\[x_{1} = - \frac{\pi}{36} + \frac{2\pi n}{3};\]

\[x_{2} = \frac{7\pi}{36} + \frac{2\pi n}{3}.\]

\[Ответ:\ \ \frac{7\pi}{36}.\]