Yeah trigonometry does become pretty trivial if you're prepared to use complex numbers and some calculus. Here in the UK we were introduced to this approach lat

Yeah trigonometry does become pretty trivial if you're prepared to use complex numbers and some calculus. Here in the UK we were introduced to this approach later on at A-level, but still had to tackle an incredible number of "solve for the missing length/angle/area" triangle problems first. (One thing the endless triangle problems do provide is practice at converting geometric problems into algebraic ones. But yes, too much of them I'd say.) I guess teachers consider complex numbers an abstraction too far in order to teach applications to geometric problems. They don't want to field endless 'woah that blows my mind' type questions about i at that stage. The downside then being that you have to memorise (or read off a cheat sheet) a lot more identities in order to manipulate things algebraically. And to convince yourself of the truth of those identities you need to rely on geometric proofs, which come more naturally to some than others. Probably makes the subject more intimidating than it should be.