Find a picture of a Unit Circle with a few rays marked on it.
Okay, maybe quite a few. It should not be hard to find this picture in your book or maybe here; The Unit Circle
For , look really hard at the ray . Compare it to the ray at . Do they have the same sine (Vertical Component)? Compare to whatever happens when you go all the way around the circle and end up in the same place. It still has the same properties as , but we not there any more. We've been around the track once. We are now at .
Many such explorations could be undertaken. Give it a little thought. It should soak in.