Решебник по алгебре и начала математического анализа 11 класс Колягин Задание 98

\[1)\arcsin(2 - 3x) = \frac{\pi}{6}\]

\[2 - 3x = \frac{1}{2}\]

\[3x = \frac{3}{2}\]

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

\[Ответ:\ \ 0,5.\]

\[2)\arcsin(3 - 2x) = \frac{\pi}{4}\]

\[3 - 2x = \frac{\sqrt{2}}{2}\]

\[2x = \frac{6 - \sqrt{2}}{2}\]

\[x = \frac{6 - \sqrt{2}}{4}.\]

\[Ответ:\ \ \frac{6 - \sqrt{2}}{4}.\]

\[3)\arcsin\frac{x - 2}{4} = - \frac{\pi}{4}\]

\[\frac{x - 2}{4} = - \frac{\sqrt{2}}{2}\]

\[x - 2 = - 2\sqrt{2}\]

\[x = 2 - 2\sqrt{2}.\]

\[Ответ:\ \ 2 - 2\sqrt{2}.\]

\[4)\arcsin\frac{x + 3}{2} = - \frac{\pi}{3}\]

\[\frac{x + 3}{2} = - \frac{\sqrt{3}}{2}\]

\[x + 3 = - \sqrt{3}\]

\[x = - 3 - \sqrt{3}.\]

\[Ответ:\ - 3 - \sqrt{3}.\]