Решебник по алгебре и начала математического анализа 11 класс Колягин Задание 861

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

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

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

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

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

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

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

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

\[= \pm \frac{3\pi}{4} + 2\pi n;\]

\[x = \frac{1}{3} \bullet \left( \pm \frac{3\pi}{4} + 2\pi n \right) =\]

\[= \pm \frac{\pi}{4} + \frac{2\pi n}{3}.\]

\[Ответ:\ \pm \frac{\pi}{4} + \frac{2\pi n}{3}.\]

\[3)\ 2\ tg\ x + 5 = 0\]

\[2\ tg\ x = - 5\]

\[tg\ x = - 2,5;\]

\[x = arctg( - 2,5) + \pi n.\]

\[Ответ:\ - arctg\ 2,5 + \pi n.\]