Phase shift

[EvoN1020v]

I am unsure which is correct:

 

e.g.

[math]

y = \cos2(x-\pi)+3

[/math]

 

Can it be defined as [math]y=\cos(2x-2\pi)+3[/math]?

 

Following the basic equation of y = AsinB(x-c)+D, does the above example means it have an vertical translation of 2 and phase shift of 2pi to the right?

 

[i know the graph will appear the exact same regardless, but I want to know which equation is more correct to draw graphs.]

[Dave]

It has a vertical translation of 3 (the +3 at the end), a phase shift of [imath]2\pi[/imath] and oscillates twice as much as a normal cos graph (the 2x).

[EvoN1020v]

Thanks Dave