InnerProductGeometry.angle_add_eq_arcsin_of_inner_eq_zero
∀ {V : Type u_1} [inst : NormedAddCommGroup V] [inst_1 : InnerProductSpace ℝ V] {x y : V},
inner ℝ x y = 0 → x ≠ 0 ∨ y ≠ 0 → InnerProductGeometry.angle x (x + y) = Real.arcsin (‖y‖ / ‖x + y‖)An angle in a right-angled triangle expressed using arcsin.
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 197 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
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
- NormedAddCommGroupstatement and proof · cited by 15,752
- Norm.normstatement and proof · cited by 5,413
- InnerProductSpacestatement and proof · cited by 3,523
- Inner.innerstatement and proof · cited by 1,089
- norm_nonnegproof · cited by 725
- Real.sqrtproof · cited by 545
- ne_of_ltproof · cited by 203
- add_sub_cancel_leftproof · cited by 198
- InnerProductGeometry.anglestatement · cited by 170
- pow_twoproof · cited by 150
- Real.arcsinstatement and proof · cited by 125
Cited by5
Results whose statement or proof uses this declaration.
- InnerProductGeometry.sin_angle_add_of_inner_eq_zeroproof · cited by 5
- InnerProductGeometry.angle_add_eq_arctan_of_inner_eq_zeroproof · cited by 4
- EuclideanGeometry.angle_eq_arcsin_of_angle_eq_pi_div_twoproof · cited by 3
- Orientation.oangle_add_right_eq_arcsin_of_oangle_eq_pi_div_twoproof · cited by 1
- InnerProductGeometry.angle_sub_eq_arcsin_of_inner_eq_zeroproof · cited by 1