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?
A) John, because ωT = 2π.
B) John, because ωT = 1 radian.
C) Larry, because ωT = 2π.
D) Larry, because ωT = 1 radian.
E) Neither, because cos(θ + 2π) = cosθ.

Question

Quizplus · Accepted Answer

Neither John nor Larry is correct because the cosine function is periodic with a period of 2π, meaning that cos(θ + 2π) = cosθ. Therefore, the value of the function after one period T does not change by 2π or by the addition of 1.00; it remains the same.

John Says That the Value of the Function Cos[ω(t