Metric distances derived from cosine similarity and Pearson and Spearman correlations

We investigate two classes of transformations of cosine similarity and and Spearman correlations into metric distances, utilising the simple of metric-preserving functions. The first class puts anti-correlated maximally far apart. Previously known transforms fall within this. The second class collates correlated and anti-correlated objects. An of such a transformation that yields a metric distance is the sine when applied to centered data.