Answer
$$\boxed{y-1/2 = \sqrt{3}/2*(x-\pi/6)}$$
Work Step by Step
To find the linearization we first need to calculate the slope by taking the derivative.
$$f'(\pi/6) = cos(\pi/6) = \sqrt {3}/2$$
We also need to find the y-value at the given $a$ value,
$$f(\pi/6) = sin(\pi/6) = 1/2$$
Since we have the point $(\pi/6, 1./2)$ and the slope $\sqrt {3}/2$, we can use point slope form.
$$\boxed{y-1/2 = \sqrt{3}/2*(x-\pi/6)}$$