Rewrite the cosine function f(x) = cos(1/3x-pi/6) as a translated cosine function.

To rewrite the function \( f(x) = \cos\left(\frac{1}{3}x - \frac{\pi}{6}\right) \) as a translated cosine function, we can use the phase shift identity between cosine and sine.

Recall that: \[ \cos\left(x - \frac{\pi}{2}\right) = \sin(x) \]

We can express \( \cos\left(\frac{1}{3}x - \frac{\pi}{6}\right) \) in terms of sine: \[ \cos\left(\frac{1}{3}x - \frac{\pi}{6}\right) = \sin\left(\frac{1}{3}x - \frac{\pi}{6} + \frac{\pi}{2}\right) \]

Now, we need to simplify \(-\frac{\pi}{6} + \frac{\pi}{2}\): \[ -\frac{\pi}{6} + \frac{\pi}{2} = -\frac{\pi}{6} + \frac{3\pi}{6} = \frac{2\pi}{6} = \frac{\pi}{3} \]

Thus, we can rewrite \( f(x) \) as: \[ f(x) = \sin\left(\frac{1}{3}x + \frac{\pi}{3}\right) \]

The correct option from the choices given is: A. f(x) = sin(1/3x + pi/3).