ANSWER
C.
[tex]y = \: \cos( \frac{2}{3}x ) [/tex]
EXPLANATION
The period of a cosine function is calculated using the formula;
[tex]T= \frac{2 \pi}{b} [/tex]
Therefore , if the period is 3π, then
[tex] \frac{2 \pi}{b} = 3\pi[/tex]
We solve b to obtain,
[tex]b = \frac{2}{3} [/tex]
This implies that, the given cosine function must have an equation of the form
[tex]y = a \: \cos( \frac{2}{3}x ) [/tex]
Among the options, the function in this form is:
[tex]y = \: \cos( \frac{2}{3}x ) [/tex]
The correct choice is C.
