We present a method to separate the longitudinal, polar, and equatorial magnetization components that may contribute to a mixed magneto-optical Kerr-effect signal and demonstrate how the spin-reorientation transition (SRT) can be investigated by means of simple Kerr magnetometry. In a Co/Au(111) film with thickness within the SRT region we find hysterisis loops with nonvanishing remanence in all three components when a field is applied within the film plane. A vertical field, however, drives the same film into a single domain state exhibiting full remanence. The fact that remanence is found in all magnetization components, and full remancence is obtained in a vertical field, rules out that the transition proceeds via a state of canting of magnetization and indicates that it proceeds via a state of coexisting phases.