A good answer might be:

Looks like the range is -1.0  ...  0.0  ...  1.0

Formula for the Angle between Two Vectors

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 au is a unit vector pointing in any direction

The angle between two unit vectors:

au · bu  =  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 (0.7071, 0.7071)T and (0.5, 0.866)T ?