'arctangent' originates from New Latin/English, specifically from the combination of Latin 'arcus' and Latin 'tangens', where 'arcus' meant 'bow, arc' and 'tangens' meant 'touching' (from 'tangere', 'to touch').

'arctangent' was formed in English by combining 'arc' (referring to an arc of a circle) and 'tangent' (a line touching a circle). The abbreviation 'arctan' and the notation 'tan^-1' developed later in mathematical usage.

Initially it referred to the arc (angle) corresponding to a given tangent; over time it came to denote the inverse tangent function that maps a number to that angle.