You should become familiar enough with the common trig angles (0°, 30°, 45°, 60°, 90°, etc) that you can convert without much thought. If you aren't there yet, just keep practicing.
For , we must ask, what angle gives a cosine of 1? This should come quickly if you think of the unit circle: (and again, if you aren't familiar with your unit circle, practice until you get good with it). In fact, any angle that is a multiple of 360° will have a cosine of 1, but since we are limited to the interval , we get
So, using your set notation,