We need to find the value of $sec(\frac{11\pi}{6})$.

1. Problem Description

We need to find the value of $sec(\frac{11\pi}{6})$.

2. Solution Steps

First, we need to find the reference angle for $\frac{11\pi}{6}$. Since $\frac{11\pi}{6}$ is in the fourth quadrant, we can find the reference angle by subtracting it from $2\pi$:

$2\pi - \frac{11\pi}{6} = \frac{12\pi}{6} - \frac{11\pi}{6} = \frac{\pi}{6}$.

The reference angle is $\frac{\pi}{6}$.

Now, we need to find the value of $cos(\frac{\pi}{6})$. We know that

$cos(\frac{\pi}{6}) = \frac{\sqrt{3}}{2}$.

Since $\frac{11\pi}{6}$ is in the fourth quadrant, cosine is positive. So,

$cos(\frac{11\pi}{6}) = cos(\frac{\pi}{6}) = \frac{\sqrt{3}}{2}$.

Now, we can find the value of $sec(\frac{11\pi}{6})$. Since $sec(x) = \frac{1}{cos(x)}$, we have:

$sec(\frac{11\pi}{6}) = \frac{1}{cos(\frac{11\pi}{6})} = \frac{1}{\frac{\sqrt{3}}{2}} = \frac{2}{\sqrt{3}}$.

3. Final Answer

The final answer is $\frac{2}{\sqrt{3}}$