[fnordpiglet]

I think geometry and trig are pretty related, and have a lot of relevance in calculus especially multivariate. To your point geometry is also the first place formal proofs take shape. That said I think geometry and trig could each be a quarter of a year long and be taught to the extent needed for almost any pursuit, with supplemental at point of need. In my education geometry and trig were two entire years, and it was so dull I lost all interest in math until I took calculus. I agree a probability course would be useful, but I don’t think probability before calculus is an awesome idea. Statistics and probability can be taught at a rudimentary level without calculus, but insight really requires calculus and linear algebra. I found taking a non calc stats and probability course made the calc version harder.

[vaidhy]

While trig is used for starting on calculus now, in practice, I never had to use trig for ML. Most of the work was in numerical differentiation and integrations. I would think trig usefulness is more in some hard sciences while ML has a much more horizontal applicability.

It is possible to teach calculus without trig (just for polynomials) and I think it is very useful just at that level.

[fnordpiglet]

It seems hard to conceive of a world where e^ix isn’t important in ML, unless that ML is sans probability, neural networks, or really most anything useful. Perhaps for regressions, so long as they have no periodic component. I think you probably can mechanically, without understanding, skate by in a job without any understanding of trig, but I don’t think you can understand much ML without it, and certainly can’t reason about limitations of an ML technique. While you might not directly use trig, I feel you must use things that were taught using trig to justify the technique and bound it’s applicability.

But really trig isn’t very complex a topic. I don’t think you should attempt to avoid teaching it. I just think it’s like a 1 month topic that is filled in as you learn calculus, linear algebra, and physics. The real intuition of trig comes form the use of it in other areas, and as a standalone subject it’s just boring.