Only a very small percentage of the population have seen truly advanced algebra.
If by advanced algebra were are still defining trig, this isn't really true. Every electrical engineer EE my age still has a couple of slide rules designed specifically for trig functions. Every computer engineer, whether an EE of not, uses trig to run R-C time calcs to time computers. Every civil engineer has to learn and be functional in it.
One of my favorite teachers was a trig genius. He would come into class each morning and put a complex circuit up on the board, list a few voltage/current parameters and then tell us he wanted all the specs on the circuit. He then left for the rest of the day, and we had to provide it all by the next day. Component specs and all the parameters of the rest of the circuit. He made masters of us in analysis, and calculus became obvious when it had to be used to specify voltages and currents all the way through the circuit at all the times it was variable. When he got done with us we all understood how to use the tools and were to how to look for mistakes in other's calcs as a team.
