Theorems · Theorem · geometry

Orientation.cos_oangle_eq_cos_angle

∀ {V : Type u_1} [inst : NormedAddCommGroup V] [inst_1 : InnerProductSpace ℝ V] [inst_2 : Fact (Module.finrank ℝ V = 2)]
  (o : Orientation ℝ V (Fin 2)) {x y : V},
  x ≠ 0 → y ≠ 0 → (o.oangle x y).cos = Real.cos (InnerProductGeometry.angle x y)

The cosine of the oriented angle between two nonzero vectors equals that of the unoriented angle.

Defined in

Mathlib.Geometry.Euclidean.Angle.Oriented.Basic

Cited by

2 results in Mathlib

Foundations

Depth 279 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceFact