According the Korean Wiki this grammar has the following meanings. If you’ve spent some time studying this grammar point you should be familiar with all of the below.
- Declaration of what you intend to do in 1st person
- Your supposition, guess or observation about something
- In the fixed 좋겠어요, 알겠어요, 모르겠어요 patterns
- Making a polite request in the form of 아/어주시겠어요?
There is however another meaning which is incredibly important, that I haven’t seen much mention of. It is used in the form of a rhetorical or hypothetical question, and most likened to the word “would” in English. It can also be used to convey sarcasm.
- 너라면 뭘 하겠어? This can be interpreted in two ways depending on the situation and your intonation.
- In the first instance you might be considering doing something but you’re not sure how to do it so you ask your friend “what would you do if you were me?”
- In the second instance you got in trouble for doing something wrong at work. You were under a lot of pressure to get it done by a deadline and you had no other option available to you, so you pushed ahead with the best way you knew. Your colleague says to you “Oh my god, why did you do it that way for?” and by replying with “너라면 뭐 하겠어?” you are saying “well (bloody hell) what would you have done then?” Here your speech would be a lot more animated and have a stronger intonation.
- 누가 그러겠어? Who would do that? This is asked sarcastically as if to say who would do such a thing?
- 내가 왜 K-Con 가겠어? 아이유를 보러 가는거지. Why would I go? This is asked sarcastically as if to say “why would I go to K-Con? What do you mean why would I ago. Isn’t it obvious I’m going to go see 아이유?”
- 네가 누구를 만나겠어? Imagine you’re having a go at your friend by saying “yeah pfft… WHO would YOU be meeting?” As if to say yeah who would wanna go on a date with you.
- 수지가 왜 Simpsons 영화를 보러 가겠어? You’re talking to your friend about a mutual friend Suzy. Your friend asks you “why is Suzy going to watch the Simpsons movie?” And you’re thinking “er… isn’t it obvious why she is going? Haven’t you seen her room, its filled with Simpsons posters. She is a Simpsons fanatic”. Therefore by saying “수지가 왜 Simpsons 영화를 보러 가겠어?” is like saying “Why do you think she’s going (duh)”
When you are asking in this form, the question can be in 1st, 2nd or 3rd person. (네가 왜 가겠어, 내가 왜 가겠어, 수지가 왜 가겠어).
When a single grammar pattern has multiple usages, I try where possible to unify their meanings. In this instance, the usage I’ve explained can be related to the second usage in the list above. For example when you are supposing something to be 맛있겠어, 재미있겠어, 덥겠어 they can all be translated to it would be delicious, it would be fun, it would be hot.
You can also translate 좋겠어 and 모르겠어 to “that would be good” and “I wouldn’t know”.