Решебник по алгебре и начала математического анализа 11 класс Алимов Задание 761

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\[1)\ y = \cos{7x}\]

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

\[\cos\left( 7 \bullet (x + T) \right) = \cos{7x}\]

\[\cos(7x + 7T) = \cos{7x}\]

\[7T = 2\pi\]

\[T = \frac{2\pi}{7}.\]

\[Ответ:\ \ \frac{2\pi}{7}.\]

\[2)\ y = \sin\frac{x}{7}\]

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

\[\sin\left( \frac{1}{7} \bullet (x + T) \right) = \sin\frac{x}{7}\]

\[\sin\left( \frac{x}{7} + \frac{T}{7} \right) = \sin\frac{x}{7}\]

\[\frac{T}{7} = 2\pi\]

\[T = 7 \bullet 2\pi = 14\pi.\]

\[Ответ:\ \ 14\pi.\]