The range is -1.0 ... 1.0
The range is minus one to plus one, because each dot product in the previous page is:
(1, 0)^{T} · ( cos θ, sin θ)^{T} = cos θ
This is true when a_{u} is a unit vector pointing in any direction.
The angle between two unit vectors:
a_{u} · b_{u} = cos θ |
where θ is the angle between the two vectors. This formula automatically includes the fact that the dot product of perpendicular vectors is zero (because cos 90° is zero).
(Calculator Problem: ) What is the cosine of the angle between the two unit vectors represented by (0.7071, 0.7071)^{T} and (0.5, 0.866)^{T} ?