Let me share a few thoughts that may or may not apply to your situation. Math MUST be approached like a foreign language: it takes study AND practice. When you have practiced and feel competent, THEN attempt the homework assignment. Homework should validate that you have mastered the concepts. Treat it like a mini-test and do not use notes or text examples.
In a trig class, I cannot imagine that the questions are tricky or “vague” (unless they are purely concept/essay type questions.) However, it would be helpful to you AND your professor to visit him during office hours. Let him know you didn’t understand the phrasing or question. Ask if most students finished the test. Also, you might want to find some study mates.
Trigonometry is usually reviewed in pre-calc and is necessary for some calculus courses (with analytical geometry.) That is probably included in applied math, but not necessarily actuarial sciences.