Question

What describes the domain of y=tanx, where n is any integer?

Answer 1

x
`\\eq` π/2 ± nπ

Explanation:

a p e x :)

Answer 2

Assuming you meant "where x is any integer":


`tan(x)` is defined as
`(sin(x))/(cos(x))`, so it would be defined for every value of
`x` except for those where
`cos(x)=0`, which is true when
`x= (\pi)/(2) +2\pi k` and
`x= (3\pi)/(2) +2\pi k`, where
`k` is some integer. These values of
`x` where
`tan(x)` is undefined are both irrational; they cannot be expressed as a ratio between two integers, and so limiting the domain to integers makes sure that we'll skip over those points every time as
`x` is increasing.

So, the domain of
`y=tan(x)`, when limiting that domain to the integers, is the set of all integers,
`\mathbb{Z}`.