Решебник по алгебре и начала математического анализа 11 класс Колягин Задание 1018

\[1)\ y = \cos\frac{3x}{2}\]

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

\[\cos\frac{3(x + T)}{2} = \cos\frac{3x}{2}\]

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

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

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

\[Ответ:\ \ \frac{4\pi}{3}.\]

\[2)\ y = 2\sin{0,6x}\]

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

\[2\sin{0,6(x + T)} = 2\sin{0,6x}\]

\[\sin(0,6x + 0,6T) = \sin{0,6x}\]

\[0,6T = 2\pi\]

\[T = \frac{2\pi}{0,6} = \frac{20\pi}{6} = \frac{10\pi}{3}.\]

\[Ответ:\ \ \frac{10\pi}{3}.\]