'arctan' originates from English, specifically the phrase 'arc tangent', where 'arc' ultimately comes from Latin 'arcus' meaning 'bow' or 'arc' and 'tangent' comes from Latin 'tangens' meaning 'touching'.

'arctan' changed from the two-word English expression 'arc tangent' used in geometry and analysis; over time the phrase was contracted in mathematical notation and speech to the shorter form 'arctan' (and sometimes abbreviated further to 'atan' in computing contexts).

Initially the phrase referred to the arc (or angle) associated with a tangent line; it evolved to denote the inverse function of tangent, i.e., the function that returns the angle whose tangent equals a given value.