Theorems · Theorem · geometry

InnerProductGeometry.sin_angle_mul_norm_mul_norm

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

The sine of the angle between two vectors, multiplied by the product of their norms.

Defined in

Mathlib.Geometry.Euclidean.Angle.Unoriented.Basic

Cited by

2 results in Mathlib

Foundations

Depth 193 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpace