which trigonometric expressions give results which are rational or expressible as surds? is there a complete set? are there infinite? for example, the well known $sin(30)=1/2$, and a range of others like $sin(45)=\sqrt2/2$, I know of, but how many are there? it seems like multiples of 30, 18, and other fractions of 360 degrees give results as surds more often.