Theorems · Definition · special functions
Real.arcsin
ℝ → ℝ
Inverse of the sin function, returns values in the range -π / 2 ≤ arcsin x ≤ π / 2.
It defaults to -π / 2 on (-∞, -1) and to π / 2 to (1, ∞).
- Cited by
- 125 results in Mathlib
- Foundations
- Depth 186 from the axioms, rests on 4,711 definitions · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Realstatement · cited by 25,697
- OrderIso.symmproof · cited by 475
- Set.IccExtendproof · cited by 26
- Real.sinOrderIsoproof · cited by 9
Cited by129
Results whose statement or proof uses this declaration.
- Complex.argproof · cited by 220
- Real.arccosproof · cited by 90
- Complex.arg_zeroproof · cited by 22
- Real.arctan_zeroproof · cited by 17
- Complex.arg_ofReal_of_nonnegproof · cited by 16
- Real.arcsin_negstatement and proof · cited by 11
- Real.arcsin_zerostatement · cited by 9
- Real.continuous_arcsinstatement · cited by 8
- Real.sin_arcsinstatement · cited by 7
- Complex.cos_argproof · cited by 7
- Real.arcsin_le_pi_div_twostatement · cited by 7
- Real.arcsin_of_le_neg_onestatement and proof · cited by 7