Question

For what intervals is `f(x) = tan((pix)/4)` continuous?

Answer 1

`tan((pix)/4)` is continuous on intervals of the form
`(2 + 4k, 2 + 4(k+1)), k in ZZ`

Explanation:

`tan(x)` is continuous on
`(pi/2 + kpi, pi/2 + (k+1)pi), k in ZZ`

So `tan((pix)/4)` is continuous where `(pix)/4` lies within such an interval. That is, where

`pi/2 + kpi < (pix)/4 < pi/2 + (k+1)pi`

Multiplying through by `4/pi` gives us

`2 + 4k < x < 2 + 4(k+1)`

Thus `tan((pix)/4)` is continuous on
`(2 + 4k, 2 + 4(k+1)), k in ZZ`