The half angle formulas used when you solve problems that are like the following I mean: Ok, they usually look something like (I may have left something out, but I am putting down the general kind of idea of how they look and work:) Something like, Find Cos A/2 if Sin A =-1/2 and SinA is in Quadrant 3 Then you have to put Cos A between these things <cosA< and then 180 goes on one side of that and 270 goes on the other side, or what have you, and then you divide 180 and 270 in half, but aren't we just dividing an angle in half, so why does that change what quadrant it's in? That is so weird? lol So what are these formulas having you do when you use them? Apparently they aren't dividing an actual angle in half. So why do they even call them half angle formulas.