Recently there was a listserv question asking for a clarification about the definition of ?phase shift? for Algebra 2/Trigonometry. This was forwarded to NYSED and here is their response.
y=A sin(Bx-C) would be re-written as y=A sin(B(x-C/B)), so the phase shift is the absolute value of (C/B). If C/B >0 then the shift is to the right. If C/B <0, then the shift is to the left. The examples help to clarify.
Examples: y=sin(2x-pi) would become y=sin(2(x-pi/2)) so the phase shift is pi/2 and the shift would be to the right.
y=cos(2x+pi/2) would become y=cos(2(x+pi/4)) so the phase shift is pi/4 and the shift is to the left because y=cos(2(x- -pi/4)).