Решебник по алгебре и начала математического анализа 10 класс Алимов Задание 768

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

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

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

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

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

\[2T = 2\pi\]

\[T = \pi.\]

\[Ответ:\ \ \pi.\]

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

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

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

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

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

\[T = 4\pi.\]

\[Ответ:\ \ 4\pi.\]