Just because triangles aren't the be-all, end-all of trigonometry doesn't mean they aren't important. We'll need to know several facts about right triangles in order to use the unit circle. While we do have an excellent, funny, and informative guide already written for you, we won't force you to read the whole thing (unless you want to).
First off, remember that the sides of a 45-45-90 right triangle are in the ratio 
, while the sides of a 30-60-90 right triangle are in a 
ratio. We haven't been able to figure out how they show up in so many places at once, though.
The other things we need are the trig functions for right triangles. That is:
Just looking at these functions brings back a lot of memories, doesn't it? Maybe they are painful, traumatic memories sometimes, but at least we remember them.
With this information in our math-solving toolbox, we're ready to tackle the unit circle. If we can force a fumble (maybe using something in that toolbox), then we can turn this game around and win one for the home team.
Or something. That's a pretty mixed-up metaphor there.