I understand the meaning of 麻烦 as "troublesome" (ex. 麻烦你等一下), but am not sure what it means in this phrase.
I've heard that this can function as some sort of apology for troubling someone. Is that true?
The term 麻烦 can be a noun, an adjective or a verb
麻烦: (n) trouble; (adj) troublesome; (v) to trouble / to bother / to inconvenience
- verb (used with object), inconvenienced, inconveniencing.
As a verb, it has to be used with object
*I understand the meaning of 麻烦 as "troublesome" (ex. 麻烦你等一下)*
No, "麻烦你等一下" means "(I have to) inconvenience you to wait a minute"
When you say 麻烦你, (inconvenience you), usually you would begin with a "sorry" .
Since 麻烦你 itself already contains an apologizing tone, the "sorry" can be omitted.
*What does 麻烦你了 means*
In this context, I prefer to translate to "could you/I, may I " before the favor speaker wants to ask from you. It's a polite form to ask for something. And the 「麻烦」is more like verb "bother".