I would check with HSLDA or a local homeschool group about any "changes" that they tell you about. Alot of times the ps really misunderstand the laws and how they pertain to hsers. I know some folks here in NY who had an issue with their district when NYS changed some requirements for graduation for ps. The district tried to tell them that they had to follow the new rules but in reality nothing changed for hsers. HSLDA cleared it up with the district quickly.
Trig is the study of triangles. Pre-cal is the study of Algebra and Trig together, sometimes known as Algebra 3. (I just looked it up on the internet to make sure.)