Question

What is the reference angle for `(14pi)/3`?

Answer 1

It is always possible to add, or subtract, `2pi` to an angle to obtain an equivalent one. The symbol `-=` in the following passages is not a real `=`, but only an equivalent symbol.

`14/3pi-2pi -= 8/3pi -= 8/3pi-2pi -= 2/3pi`.

`2/3pi` is just `pi/3` less that `pi` so the acute angle (the reference angle) between `2/3 pi` and the horizontal is `pi/3`

Because they are coterminal, the reference angle for `14/3pi` is the same. It is `pi/3`.