John says that the value of the function cos[ω(t + T) + ϕ], obtained one period T after time t, is greater than cos(ωt + ϕ) by 2π. Larry says that it is greater by the addition of 1.00 to cos(ωt + ϕ). Which one, if either, is correct?

Respuesta :

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].

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