John Says That the Value of the Function Cos[ $\omega$

Multiple Choice

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

A) John,because $\omega$ T = 2 $\pi$ .
B) John,because $\omega$ T = 1 radian.
C) Larry,because $\omega$ T = 2 $\pi$ .
D) Larry,because $\omega$ T = 1 radian.
E) Neither,because cos( $\theta$ + 2 $\omega$ ) = cos $\theta$ .