NOTE 1 The term "instantaneous phase" is only used when the independent variable is time.
NOTE 2 For the quantity a(t)= A ^ cos(ω t+ ϑ 0 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaaiaadggacaGGOaGaam iDaiaacMcacqGH9aqpceWGbbGbaKaajugabiGacogacaGGVbGaai4C aOGaciikaiabeM8a3jaayIW7caWG0bGaey4kaSIaeqy0dO0aaSbaaS qaaKqzadGaaGimaaWcbeaakiaacMcaaaa@4817@ , the phase is ω t+ ϑ 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaaiabeM8a3jaayIW7ca WG0bGaey4kaSIaeqy0dO0aaSbaaSqaaKqzadGaaGimaaWcbeaaaaa@3E52@ .