Question

Question #fa041

Answer 1

`D = uuu_(n in ZZ)(2pin, pi+2pin)`

Explanation:

As sine is periodic with a period of `2pi` and is positive on `(0, pi)`, we have that `sinphi > 0 <=> phi in (2pin, pi+2pin)` for some `n in ZZ`.

Just like how we can use `sum` to denote repeated addition or `prod` to denote repeated multiplication, we can use `uuu` to denote repeated unions. Thus, to express the set of all values on which sine is positive, we can write it as the union of all intervals of the form `(2pin, pi+2pin)` for some integer `n`, i.e.

`D = uuu_(n in ZZ)(2pin, pi+2pin)`