say cos^{-1}(3/5). As far as this particular question, cos(x)= -1/\sqrt{2}, if, as you say, you know "(pi/4, pi/3, etc.)" then this should be easy. cos(t) is the x coordinate of a point on the unit circel so draw a vertical line at x= -1/\sqrt{2} and think about the symmetry of the circle...
I hope this helped.. I tried my best, I'm not sure if this is what you're looking for but I'm not that good at math. I'm sorry. But good luck!
