The term cosine distance is often used for the complement in positive space, that is: formula_2 where formula_3 is the cosine distance and formula_4 is the cosine similarity. It is important to note, however, that this is not a proper distance metric as it does not have the triangle inequality property—or, more formally, the Schwarz inequality—and it violates the coincidence axiom; to repair the triangle inequality property while maintaining the same ordering, it is necessary to convert to angular distance (see below).