Theorems · Theorem · special functions
Real.sin_arccos
∀ (x : ℝ), Real.sin (Real.arccos x) = √(1 - x ^ 2)
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 192 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Nat.cast_oneproof · cited by 2,501
- LT.lt.leproof · cited by 2,189
- Nat.cast_zeroproof · cited by 1,870
- le_of_ltproof · cited by 1,175
- Real.sqrtstatement and proof · cited by 545
- le_of_not_gtproof · cited by 430
- Real.sinstatement and proof · cited by 389
- not_leproof · cited by 328
- Real.arcsinproof · cited by 125
- Real.arccosstatement · cited by 90
- mul_nonneg_of_nonpos_of_nonposproof · cited by 45
Cited by2
Results whose statement or proof uses this declaration.
- Real.arccos_eq_arcsinproof · cited by 2
- InnerProductGeometry.sin_angle_mul_norm_mul_normproof · cited by 2