I've been told that essentially the more (으)시's you put in, the more polite you're being. As with English, if you go super-polite, you might be in danger of over-egging the pudding, or sounding insincere - but it will still make sense.
One '(으)시' is enough to show politeness:
선생님이 보내신 분 입니까?
선생님이 보낸 분 이십니까?
If you wanted to level up the politeness, ...
Saying that the -는 ending creates an adjective can be a bit confusing. Technically, it creates a participle, which is the form of the verb which acts like an adjective, that is, by modifying a following noun.
These are primarily used in Korean to create relative clauses, for example:
멀리 보는 사람들이 성공할 수 있다
People who see far ahead can be successful
I found a similar question and answer here: (Korean)
It says that Though it differs by scholars, ㅅ in medival Korean had two usage: 관형격 조사(冠形格 助詞, adnominal case postposition) and 사이시옷.
Hope it helps others who are ...
noun + 적 : it has two usage : noun and adnominal (or pre-noun)
1) For instance, 철학적 사고 = philosophical thought
It is adnominal whose meaning is being related with philosophy.
2) 철학적인 분석 = philosophical analysis.
It is a noun whose meaning is a thing related with philosophy. Here
철학적 (noun) + 인 = adjective.
@ He is philosophical 그는 철학적이다.
철학적인 그는 (O) ...