Final answer:
The period of the function cos(x/2) is 4π, obtained by dividing the standard cosine function period of 2π by the coefficient of x, which is 1/2.
Step-by-step explanation:
To determine the period of the function cos(x/2), we recall that the standard cosine function cos(x) has a period of 2π. The period of a function is the length of one complete cycle of the function, and for cosine, this is the interval on the x-axis for which the function repeats its values.
When the cosine function is altered to cos(x/2), the period is obtained by dividing the standard period by the coefficient of x. In this case, since the coefficient is 1/2 (because x is divided by 2), we divide the standard period of 2π by 1/2, giving us a new period of 4π. Thus, the period of the function cos(x/2) is 4π (Option D).