was helping my kid with trig, he had a problem like sec(pi/4*x -pi/2) and it wanted the period and the phase shift.
now words aren't always uniformly defined even in math, but to my mind this thing has period 8, and phase shift pi/2 but he wanted to say phase shift was 2 based on rewriting the argument as pi/4*(x-2)
which would you expect to be the definition of phase shift in a precalculus text?
@dlakelan I think he would be "right" under most definitions. Phase is only measured as a standalone when you can write the first piece as a 2*pi*x structure.
If you think of it as a translation in x, followed by a transformation in x, then transformation in y, then translation in y, that's the convention for taking a default trig function to a modified form. So you work in reverse to return it to standard form, then read off the A,B,C,D from A*trig(B*x + C) + D.
@dlakelan so in his case:
* sec(x)
* sec(x-2)
* sec(pi/4(x-2))
Fin.
There's no amplitude transformation or vertical translation. A=D=1.
Daniel Lakeland
Wesley Burr