Taking PreCalculus 12 and Calculus 12 at the same time?

There actually isn't much in precalc that is required in calc. Precalc is more to get people comfortable with different types of functions and transformations where calc is about how functions change. You may see functions that you're unfamiliar with in calc, but towards the end of the course, hopefully everything will fit together for you.

Some functions you'll see in calc that's introduced in precalc:

log, ln, exp, sin, cos, tan, sec, csc, cot... that's all that comes to mind

if you have already taken trig, then it is possible to take both in the same semester. but why? in the dark ages, when I went to school, there was no precalculus class. After trig, you took calculus. I have taught precalculus. much of it was just a review of algebra and trig. "modern" algebra 2 classes are inadequate, because they leave out some topics and these are then introduced in precalc. If they were taught in alg 2 there would be no need for precalc.

What I am trying to say, IF you had a really good alg 2 course and a really good trig course then precalc.is unnecessary.

Seems pretty strange. There's a reason they call it PRE-calc. You school does a rotten job with scheduling. Talk to the teacher to find out if it's OK to take them together. It might be, but would probably be better to take them sequentially. "Class is full" is a lame excuse. They can probably squeeze in 1 more. Maybe someone in first semester pre-calc class isn't taking calc in the 2nd semester, and could switch with you.