arcsin range and domain: [−1, 1] → [−π/2, π/2]
arcsin takes inputs in [−1, 1] and returns angles in [−π/2, π/2]. Sine repeats, so it has no true inverse until the range is restricted this way - which is why a calculator's arcsin never returns an obtuse angle, and why the Law of Sines' ambiguous case needs checking by hand.
Related Inverse identities
Common questions
What is the arcsin range identity?
arcsin takes inputs in [−1, 1] and returns angles in [−π/2, π/2]. Sine repeats, so it has no true inverse until the range is restricted this way - which is why a calculator's arcsin never returns an obtuse angle, and why the Law of Sines' ambiguous case needs checking by hand.
Which identities are related to arcsin range?
arcsin range belongs to the Inverse group. The identities used alongside it most often are arccos range and arctan range.
Practise it
Reading a formula is not the same as recalling it under time pressure. The workspace drills Inverse questions in the quiz, and the triangle solver shows a worked solution for any triangle you type in.
Or browse all 45 identities in the full reference, or read the trigonometry guides for the method behind them.