I have attached a pdf document containing the vast majority of trigonometry I have needed to know on a working basis. The first page consists of trigonometry I think everyone should have memorized. I have never needed to have anything more than the first sheet memorized for any application. The second page is a non-exhaustive sheet of most of the trigonometric identities that I have found useful, and a few more besides.
It is my opinion that a student who memorizes the first sheet, and can derive anything on the second sheet, has a fairly good grasp of trigonometry.
I hope this proves useful.