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
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.