Sentence-initial 咳 is a sigh of resignation or mild frustration — closer to English 'oh well' or 'sigh' than to a sharp 'hey'. It typically prefaces complaints or rueful admissions.
usage
Compare with neighbouring sighing interjections 唉 and 哎. 咳 tends to carry the heaviest resignation; 唉 sounds more weary; 哎 is lighter and often surprised.
Left radical 口 marks the character as a mouth-action — fitting for an interjection, a noise that comes out of the mouth. The same 口 groups 咳 with other vocal sounds like 唉 (sigh), 哎 (hey), 嗯 (hm).
