Answer
The exact value of the provided expression is $\frac{\sqrt{3}}{2}$.
Work Step by Step
We know that the reference angle for $\theta =\frac{11\pi }{6}$ is:
$\begin{align}
& \theta '=2\pi -\frac{11\pi }{6} \\
& =\frac{12\pi -11\pi }{6} \\
& =\frac{\pi }{6}
\end{align}$
Now, the function value for the reference angle is:
$\cos \frac{\pi }{6}=\frac{\sqrt{3}}{2}$
Thus, we see that the angle $\frac{11\pi }{6}$ lies in quadrant IV, so the cos function is positive:
$\begin{align}
& \cos \frac{11\pi }{6}=\cos \frac{\pi }{6} \\
& =\frac{\sqrt{3}}{2}
\end{align}$
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