Решебник по алгебре и начала математического анализа 11 класс Колягин Задание 125

\[1)\ y = 2\sin(2x + 1)\]

\[y(x + T) = y(x)\]

\[2\sin(2x + 2T + 1) = 2\sin(2x + 1)\]

\[\sin(2x + 1 + 2T) = \sin(2x + 1)\]

\[2T = 2\pi\]

\[x = \pi.\]

\[Ответ:\ \ \pi.\]

\[2)\ y = 3\ tg\frac{1}{4}(x + 1)\]

\[y(x + T) = y(x)\]

\[3\ tg\frac{1}{4}(x + T + 1) = 3\ tg\frac{1}{4}(x + 1)\]

\[\text{tg}\left( \frac{x + 1}{4} + \frac{T}{4} \right) = tg\frac{x + 1}{4}\]

\[\frac{T}{4} = \pi\]

\[T = 4\pi.\]

\[Ответ:\ \ 4\pi.\]