Решебник по алгебре и начала математического анализа 10 класс Колягин Задание 1171

\[\boxed{\mathbf{1171}\mathbf{.}}\]

\[\sin{2x} = \frac{1}{2}\ \]

\[2x = ( - 1)^{n} \bullet \arcsin\frac{1}{2} + \pi n =\]

\[= ( - 1)^{n} \bullet \frac{\pi}{6} + \pi n\]

\[x = \frac{1}{2} \bullet \left( ( - 1)^{n} \bullet \frac{\pi}{6} + \pi n \right)\]

\[x = ( - 1)^{n} \bullet \frac{\pi}{12} + \frac{\text{πn}}{2}.\]

\[\lbrack 0;\ 2\pi\rbrack:\]

\[x_{1} = \frac{\pi}{12};\]

\[x_{2} = - \frac{\pi}{12} + \frac{\pi}{2} = \frac{5\pi}{12};\]

\[x_{3} = \frac{\pi}{12} + \frac{2\pi}{2} = \frac{13\pi}{12};\]

\[x_{4} = - \frac{\pi}{12} + \frac{3\pi}{2} = \frac{17\pi}{12}.\]