We take the lowermost point - O.
The previous point - A, and following - B.
Let q = cos (corner between AO and axis OX)
r = cos (corner between BO and axis OX)

If q < r then ccw
 else cw

I got AC!!!

Simple but wrong!

Simple test:

3
4 4
1 1
3 5

Your answer is ccw, but correct cw.
Another proof that timus test are weak :(

  The method which find  the lowermost point is right...
  But don't use cos & sin, think another way :)

MY! solution is simple)
only 6 actions for every Vertex. Don't use sin or cos

....
3
4 4
1 1
3 5=cw?Have you ever seen any clocks?