Answer:
No one is right
Explanation:
John Case:
The function [tex]cos(\omega t +\phi)[/tex] is defined between -1 and 1, So it is not possible obtain a value [tex]2\pi[/tex] greater.
In addition, if you move the function cosine a T Value, and T is the Period, the function take the same value due to the cosine is a periodic function.
Larry case:
Is you have [tex]f=1+cos(\omega t +\phi)[/tex], the domain of this is [0,2].
it is equivalent to adding 1 to the domain of the [tex]f=1+cos(\omega t +\phi)[/tex], and its mean that the function [tex]f=cos(\omega t +\phi)[/tex], in general, is not greater than [tex]cos(\omega t +\phi)[/tex].