Задача 11. Решите уравнение: \({\sin ^2}x = \dfrac{1}{4}\)
ОТВЕТ: \( \pm \dfrac{\pi }{6} + \pi k;\quad \,k \in Z.\)Ответ
\({\sin ^2}x = \dfrac{1}{4}\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\left[ {\begin{array}{*{20}{c}}{\sin x = \dfrac{1}{2},}\\{\sin x = -\dfrac{1}{2}}\end{array}\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\,} \right.\left[ {\begin{array}{*{20}{c}}{x = \dfrac{\pi }{6} + 2\pi k,\,\,\,\,\,}\\{x = \dfrac{{5\pi }}{6} + 2\pi k,\,\,\,}\\{x = -\dfrac{\pi }{6} + 2\pi k,\,\,\,}\\{x = -\dfrac{{5\pi }}{6} + 2\pi k\,}\end{array}\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,} \right.x = \pm \dfrac{\pi }{6} + \pi k,\,\,\,\,\,\,\,\,k\, \in \,Z.\) Ответ: \( \pm \dfrac{\pi }{6} + \pi k;\quad \,k \in Z.\)Решение