Cogently means “in a cogent way”: you set out your reasons so they are clear, well ordered, and hard to brush aside. It is the how of the speaking or writing, not a new meaning of its own. You will meet it in formal writing: “She argued cogently that…” Everyday English more often says “clearly” or “convincingly,” though those are a little looser. “Clearly” can just mean easy to hear or easy to see; cogently still carries the sense of a case that holds together. You almost never need it in casual talk. If you use it at the dinner table, it will sound like a book — which is fine in an essay.

有說服力地、中肯地