[photonemitter]

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

[Ma8ee]

Oh, I don’t have problems deriving the Taylor expansion of anything. It’s just that when I need it my main focus is on something else. My productivity has increased a lot since I started putting those often used things in Anki so I used could use them without having to look them up or derive them every time.

[photonemitter]

Of course. Yeah, what I was trying to illustrate is that with enough contextual knowledge the amount of things one has to memorize becomes comparatively smaller. Basically if one learns and remembers Euler's Identity and the expansion of e^x = (x^n)/(n!), then you don't really need to memorize the trigonometric expansions.

Reading over it I guess that may have been your initial point.