Inverse

arccos range and domain: [−1, 1] → [0, π]

arccos:[1,1][0,π]\arccos : [-1, 1] \to [0, \pi]

arccos takes inputs in [−1, 1] and returns angles in [0, π]. That range covers every angle a triangle can have, which is why the Law of Cosines never suffers an ambiguous case while the Law of Sines does.

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.