cos(30) = cos(-30)
as -30 is a reflection in the x-axis. Also
cos(150) = -cos(30)
as 150 is a reflection in the y axis.
I think part of the problem stems from students not really being taught why the cast system works, in terms of considering eg what sin(100) actually means. Since sin = opp/hyp, how is it even possible to have a right angled triangle with a 100 degree angle in it?