More importantly, the definition of the cosine is given by projecting a unit vector onto a given directed line, and then measuring the length of the projection.
The way to find a given cosine of a given angle between two arbitrary vectors is by taking the dot product of the two vectors and then normalizing by their lengths.
Using the cosine to define the dot product is precisely backwards.
The way to find a given cosine of a given angle between two arbitrary vectors is by taking the dot product of the two vectors and then normalizing by their lengths.
Using the cosine to define the dot product is precisely backwards.