The usage of 'Arcane' has significantly increased over the years (until the bimillennial), in literary materials. This Ngram shows the frequency of usage of 'Arcane' from written materials, spanning from 1800 to 2008. Although the word is not that frequently used in day-to-day conversations, the word may be used somewhat commonly in historical terms and theoretical literature.
To understand the word better, why don't you look into the history and origin of the word:
1540s, from Latin 'arcanus' "secret, hidden, private, concealed," from 'arcere' "to close up, enclose, contain," from arca "chest, box, place for safe-keeping," from PIE root *ark- "to hold, contain, guard" (source also of Greek 'arkos' "defense," 'arkein' "to ward off;" Armenian 'argel' "obstacle;" Lithuanian raktas "key," rakinti "to shut, lock").
As per your way of learning the word, that depends on one person to another. You used this to learn the word:
"Referring to "arc and e" in mathematics, which is arcane to students."
But I wouldn't learn this word using your method, I would relate it to "Arcanine", which happens to be a mysterious and enigmatic Pokemon. But that's just me. The way a person learns a new word is by relating it to something he personally knows. This can be influenced by another person's thought process, but it generally comes from within you. This part of the question is primarily opinion-based.