To adequately evaluate a student studying for trigonometry, the teacher should review their progress with the subject material, observe their use of problem solving strategies, and evaluate their understanding of the concepts. Additionally, the teacher should provide feedback to the student on areas which could use improvement. The evaluation should consider both their efforts in class, as well as their performance on tests and assignments. The teacher should also take into account the student's overall level of interest in the subject and the amount of effort they are putting into furthering their understanding of the material.