Yes my good sir, you are correct.

And just to help you along, here's an alternative method to do the question.

If , then you may construct the right-angled with that ratio.

|\

| \

1 | \ 3

| \

|____\

So }.

But since the desired range is

use the identity , to get the desired result

Forgive my very shoddy triangle please. It's almost 11p.m.