I really just want to verify this for peace of mind, as I am beyond certain of my answer (I even ran it through C++ to verify my answer):

$\displaystyle \sqrt{(-2sin2t)^2 + (2cos2t)^2} = 2$, simple enough right?

however the solutions shows it to be equal to4. (Headbang)

Surely this is a mistake unless I'm completely missing something here.