If we changed symbols now, it would create an even bigger mess. Because the people that learn the new symbols, could not read any textbook published before 0 A.D. (Anno Discombobuli)
Sure, back then when everybody who learned trigonometry had a classical education with ancient greek picking greek letters when the latin alphabet wouldn't do was a rational decision. It just hasn't aged well.
Virtually all the textbooks use those symbols. Do you have a viable and better alternative to suggest or are you just complaining? And I didn't assume that you know or don't know something, I just wrote it down for the sake of the argument. We are not having a private conversation, we are contributing to a public discussion.
Math also uses made up symbols specific to math a lot (integral, summations, arrows, operators...).
If you want to claim that Greek is the problem, how would you solve the problem of insufficient symbols?
Adding another alphabet alleviates those issues somewhat but even with greek letters added in we still run into this issue somewhat commonly.
Btw, even mathematicians don't mind writing out `sin` or `cos` or `ln` in their formulas. So they are certainly not completely averse to multiple letters.
Agreed. But yet... some of the approaches taken to deal with that can be wildly annoying. Actually, using the Greek letters is probably the best of the lot, since they are a completely different set of characters with known pronunciations.
OTOH, sometimes you'll see people use both upper-case and lower-case latin letters in the same problem, forcing you to read it in stilted language like "The derivative of Big X with respect to y, plus the integral of Little x ..." Aaarrgggh.[1]
And then you get the "stylized" letters, which are (mostly) just Latin letters, but have no obvious unique pronunciation or verbalization without going through contortions. I mean, what do you say for "𝔑" especially if there is also a "n" on the page? And who's even going to recognize these monstrosities unless you're already a mathematician: 𝔖, 𝔚, 𝖄? Aaarrggggghhh.
[1]: to be fair, you could have the same problem with mixed case of Greek letters, but I haven't seen that as a common problem. But maybe that's only because I'm not a mathematician. shrug
For example the convention to use the greek alphabet for certain things. This is totally arbitrary and you could have also used emoticons instead (had they existed). But what this means is that the pupil, before tackling the meat of the mathematical problem has to accept that weird looking letter they have never seen for no real reason whatsoever.
And I say that as someone who can fluently read the greek alphabet.