'arcsine' originates from Modern English, specifically the combination of the words 'arc' and 'sine', where 'arc' meant 'a circular arc' (from Latin 'arcus') and 'sine' referred to the trigonometric sine (from Latin 'sinus').

'sine' changed from Sanskrit 'jya-' (via Arabic 'jayb') into Latin 'sinus', and later became the mathematical term 'sine' in European languages; 'arc' comes from Latin 'arcus' via Old French 'arc'; these elements were combined in Modern English to form 'arcsine' to denote the inverse of the sine function.

Initially, Latin 'sinus' meant 'bay' or 'fold', but over time it came to denote the trigonometric sine; combining 'arc' and 'sine' produced 'arcsine', which now specifically means 'the inverse of the sine function' in mathematics.