Найди область определения для каждой функции. y=\tg (x+\frac{\pi }{4}). x\ne \frac{\pi }{4}+\pi n,n \in Z x\ne \frac{\pi }{2}+\pi n,n\in Z x\ne 4{\pi }+\pi n,n\in Z x\ne \frac{\pi }{8}+\pi n,n\in Z y=\frac{1}{\tg 3x}. x\ne \frac{\pi n}{4}+\pi n,n\in Z x\ne \frac{\pi }{6}+\pi n,n\in Z x\ne \frac{\pi }{3}+\pi n,n\in Z x\ne \frac{\pi n}{6},n\in Z y=\ctg (x-\frac{\pi }{4}). x\ne \frac{\pi }{4}+\pi n,n\in Z x\ne \frac{\pi }{2}+\pi n,n\in Z x\ne 4{\pi }+\pi n,n\in Z x\ne \frac{\pi }{8}+\pi n,n\in Z y=\frac{1}{\ctg x}. x\ne \frac{\pi n}{4}+\pi n,n\in Z x\ne \frac{\pi }{4}+\pi n,n\in Z x\ne \frac{\pi }{2}+\pi n,n\in Z x\ne \frac{\pi n}{2},n\in Z

Задание

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Найди область определения для каждой функции.

\(y=\tg (x+\frac{\pi }{4})\) .

\(x\ne \frac{\pi }{4}+\pi n,n \in Z \)
\(x\ne \frac{\pi }{2}+\pi n,n\in Z \)
\(x\ne 4{\pi }+\pi n,n\in Z \)
\(x\ne \frac{\pi }{8}+\pi n,n\in Z \)

\(y=\frac{1}{\tg 3x}\) .

\(x\ne \frac{\pi n}{4}+\pi n,n\in Z \)
\(x\ne \frac{\pi }{6}+\pi n,n\in Z \)
\(x\ne \frac{\pi }{3}+\pi n,n\in Z \)
\(x\ne \frac{\pi n}{6},n\in Z \)

\(y=\ctg (x-\frac{\pi }{4})\) .

\(x\ne \frac{\pi }{4}+\pi n,n\in Z \)
\(x\ne \frac{\pi }{2}+\pi n,n\in Z \)
\(x\ne 4{\pi }+\pi n,n\in Z\)
\(x\ne \frac{\pi }{8}+\pi n,n\in Z \)

\(y=\frac{1}{\ctg x}\) .

\(x\ne \frac{\pi n}{4}+\pi n,n\in Z \)
\(x\ne \frac{\pi }{4}+\pi n,n\in Z \)
\(x\ne \frac{\pi }{2}+\pi n,n\in Z \)
\(x\ne \frac{\pi n}{2},n\in Z \)