I'm helping a 9th grader review for his Algebra 2 Regents exam (New York State). They need to know how to find the "reference angle." (I did read Why teach reference angles?.)
I haven't found a simple reason that he will be able to relate to at his current stage, for why we would need or want the reference angle.
If there is one, please explain.
If there isn't one, that's okay, he understands that the educational system does involve some senseless hoops to go through.
Historical context could be interesting.