Ahhh, the dreaded "figure the 6 trig functions out by hand" request.
It's not that bad!!! :-)
Essentially, there are only 5 angles they are going to ask for, who only can result in 5 absolute values for sine and cosine, and only 2 triangles you need to know (of which, one is pretty obvious). Then, with knowing which quadrant your angle is in, you are golden!
See the video for more. :-)