Решебник по алгебре и начала математического анализа 11 класс Алимов Задание 705

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

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

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

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

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

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

\[Ответ:\ \ 5\pi.\]

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

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

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

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

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

\[T = 2\pi \bullet \frac{2}{3} = \frac{4\pi}{3}.\]

\[Ответ:\ \ \frac{4\pi}{3}.\]

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

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

\[\text{tg}\left( \frac{1}{2} \bullet (x + T) \right) = tg\frac{x}{2}\]

\[\text{tg}\left( \frac{x}{2} + \frac{1}{2}T \right) = tg\frac{x}{2}\]

\[\frac{1}{2}T = \pi\]

\[T = 2\pi.\]

\[Ответ:\ \ 2\pi.\]

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

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

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

\[Первое\ уравнение:\]

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

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

\[T = \pi.\]

\[Второе\ уравнение:\]

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

\[T = 2\pi.\]

\[Ответ:\ \ \pi.\]