Let's have a look here:
Notice that they all have 2's as denominators, which cuts down the difficulty of remembering these by half (get it?), with the exception of π/4, whose denominators are √2―no big deal.
All I do to remember these is say to myself: "1, 3, 1" twice. Whether you start at 0π (or 2π) or π/2, this pattern will work.
Now, the other three quarters of the circle are easy to coordinate if you know these three (I exclude the 0, 90, 180, 270 and 360 degrees because they are obvious). Just remember that the quadrants (from 1st to 4th, (cos, sin)) go like this: (+,+), (-, +), (-,-) and (+, -).
There you go, a perfectly and exactly coordinated circle!