Question

For the function f(x) = 2(cos(x - 5π/6)), find the midline.

a) x = π/3
b) x = -5π/6
c) x = 5π/6
d) x = 0

Answer 1

The midline of the function f(x) = 2(cos(x - 5π/6)) is y = 0, so the correct answer is d) x = 0, as midline refers to a y-value.

Step-by-step explanation:

The midline of a trigonometric function like
`f(x) = 2(cos(x - 5(\pi)/(6)))` represents the horizontal shift of the cosine function. Considering that the standard cosine function, cos(x), has a midline at y = 0, any vertical shift would alter this midline. However, since this function does not have a vertical shift (no constant is added to the function), the midline of the transformed function remains unchanged at y = 0. Therefore, the correct answer is d) x = 0, as midline refers to a y-value, not an x-value, and in this case, it is the y-value where the function oscillates around.