I'm having trouble understanding why I was taught the way I was today when finding an answer to this problem is so much easier. Can someone thoroughly explain to me why?

I have to evaluate

cos(2pi / 3)

Basically what I do is, I look at a unit circle and see what x value is for (2pi/3) and I find (-1/2). Done that is the answer according to my book.

The method my teacher told us we should do seems like its a few extra steps only to arrive at the answer I get just from directly looking at a Unit Circle chart.

He tells us we need to first find the reference number for (2pi / 3) which is (pi / 3). Then since (2pi / 3) is in quadrant II, the cos(2pi / 3) is gonna be negative. From here we use the reference number and the fact it's negative to achieve...

-cos (pi / 3) = (-1/2)

It is the same answer as the method I do it which is simple. I mean I don't mind doing it the way he taught us except i'm tryin got understand what is the significance of doing it his way if i can do it my way and still get the same answer every single time.