Describe the period of the function f(x) = 2cos(1/6x +π/3) (1 point) Responses π3 pi over 3 2π 2 pi 12π 12 pi −π3
The period of a function is the length of the interval over which it repeats its values. For the given function f(x) = 2cos(1/6x + π/3), the period can be determined by looking at the coefficient of x inside the cosine function.
In this case, the coefficient of x is 1/6. The period of the function is given by the formula:
Period = 2π / (absolute value of the coefficient of x)
So, the period of the given function is 2π / (1/6) = 12π.
Therefore, the correct response is 12π or 12 pi.