InnerProductGeometry.sin_eq_one_iff_angle_eq_pi_div_two
∀ {V : Type u_1} [inst : NormedAddCommGroup V] [inst_1 : InnerProductSpace ℝ V] {x y : V},
Real.sin (InnerProductGeometry.angle x y) = 1 ↔ InnerProductGeometry.angle x y = Real.pi / 2The sine of the angle between two vectors is 1 if and only if the angle is π / 2.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 192 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites14
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
- InnerProductSpacestatement and proof · cited by 3,523
- Real.pistatement and proof · cited by 1,774
- sub_selfproof · cited by 996
- Real.sqrtproof · cited by 545
- one_powproof · cited by 521
- Real.sinstatement and proof · cited by 389
- InnerProductGeometry.anglestatement and proof · cited by 170
- Real.sin_pi_div_twoproof · cited by 29
- Real.sqrt_zeroproof · cited by 28
- abs_eq_zeroproof · cited by 17
Cited by1
Results whose statement or proof uses this declaration.
- EuclideanGeometry.sin_eq_one_iff_angle_eq_pi_div_twoproof · cited by 0