Question

How do you find the period for `y = -tan(x - pi/2)`?

Answer 1

The period is always `pi` in this case:

If you add a constant inside the brackets or multiply by a constant outside the period of a periodic function doesn't change, this is trivial:

if `f` has period `T`:
1)`f(x+T)=f(x) => f(x+T+a)=f((x+a)+T)=f(x+a)` so the period of `f(x+a)` is still `T` (you know it's minimal because it's minimal in `f`)
2) `f(x+T)=f(x) => af(x+T)=af(x)`, and still it's minimal because it's minimal in `f`

so the period is `pi`, the same as in `tan(x)`