Theorems · Theorem · geometry

InnerProductGeometry.sin_angle

∀ {V : Type u_1} [inst : NormedAddCommGroup V] [inst_1 : InnerProductSpace ℝ V] {x y : V},
  x ≠ 0 →
    y ≠ 0 →
      Real.sin (InnerProductGeometry.angle x y) = √(inner ℝ x x * inner ℝ y y - inner ℝ x y * inner ℝ x y) / (‖x‖ * ‖y‖)

The sine of the angle between two vectors.

Defined in

Mathlib.Geometry.Euclidean.Angle.Unoriented.Basic

Cited by

1 results in Mathlib

Foundations

Depth 194 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpace