@CrimsonWife Actually, it is very common for kids to have Alg II and not have had trig ( Happened to one of my kids). Trig can be learned very quickly through an online source ( or Summer study) so the kid can move on to Pre-Calc. Also, independent study in math is a positive not a negative. IF the child is very advanced they can modify the study to accommodate future plans. It’s also extremely likely that your child won’t be alone. There are usually a handful of kids so kid might even be in an independent study that connects with others.
Most Asian kids at my kids BS start in Pre-Calc so many are even more advanced than Pre-Calc Freshman year . IF the school won’t allow your child to accelerate unless they meet all standards ( trig, for example), it’s likely your child is going to be bored repeating the same material. And have someone who knows math check out the curriculum. I had my spouse (who was a math major at one point) check it out. Was able to read what it actually entailed. Some programs were apparently much better than others. And your kid might have ideas based on material they have already covered. Mine did. And filling in CS/Engineering isn’t a math.
Ask the math deptment to put in writing the expected sequence for your child, if accepted. It might/might not suit.