Решебник по алгебре и начала математического анализа 11 класс Колягин Задание 18

\[1)\ y = \cos{\frac{2}{5}x}\]

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

\[\cos\left( \frac{2}{5}x + \frac{2}{5}T \right) = \cos{\frac{2}{5}x}\]

\[\frac{2}{5}T = 2\pi\]

\[T = 5\pi.\]

\[Ответ:\ \ 5\pi.\]

\[2)\ y = \sin{\frac{3}{2}x}\]

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

\[\sin\left( \frac{3}{2}x + \frac{3}{2}T \right) = \sin{\frac{3}{2}x}\]

\[\frac{3}{2}T = 2\pi\]

\[T = \frac{4\pi}{3}.\]

\[Ответ:\ \ \frac{4\pi}{3}.\]

\[3)\ y = tg\frac{x}{2}\]

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

\[\text{tg}\left( \frac{x}{2} + \frac{T}{2} \right) = tg\frac{x}{2}\]

\[\frac{T}{2} = \pi\]

\[T = 2\pi.\]

\[Ответ:\ \ 2\pi.\]

\[4)\ y = \left| \sin x \right|\]

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

\[\left| \sin(x + T) \right| = \left| \sin x \right|\]

\[\sin(x + T) = \pm \sin x\]

\[T = 2\pi\]

\[T = \pi.\]

\[Ответ:\ \ \pi.\]