Yes, absolutely. In many/most real world cases, different types of learning overlap (these themselves are only mental models, after all). In this case, the cognitive aspect would be the what and why, helping you to get why this exists, what problem this solves, and to how to find out whether the current problem at hand is a good case for an application of this knowledge. And if your mental model is precise enough (say if you have 2 decades of experience as a full-time mathematician), you'd probably be able to recreate the function as needed.

Everyone else still has to memorize the actual terms.

taylor of e goes something like 1 + x + x^/2! + x^3/3!...

Well if we look at cos and sin, we know that these correspond to e^x if x = i x So then it’s easy to plug that in to the expression for e and get e^{i x} = 1 + ix - x^2/2! - i x^3/3! ... Taking the imaginary part gives us sin, and taking the real gives us cos.

So all we have to remember really is the pattern for e and to put ix instead of x. e^(ix) = sum((1/n!) * (ix)^n)

This was the Aha! that I got from a professor in my bachelors. Of course there’s still like two or three things to remember, but it’s a whole lot easier to unpack from there than to memorize the expansion of cos

I agree. Strong emotions cause memories to imprint deeply. I would argue that the "lightbulb moment" may use this effect.