Evaluate each expression.
$\(\cot\[\left\)(\(\frac{11\pi}{6}\]\right\))$

• A. $\(\frac\)12$
• B. $-\(\frac{\sqrt3}{3}\)$
• C. $-\(\sqrt\)3$
• D. $2$

Answer: (C)

Verified step by step guidance

1. Identify the angle: The angle given is \( \frac{11\pi}{6} \). This angle is in radians and is located in the fourth quadrant of the unit circle.
2. Determine the reference angle: The reference angle for \( \frac{11\pi}{6} \) is \( 2\pi - \frac{11\pi}{6} = \frac{\pi}{6} \).
3. Recall the cotangent function: The cotangent of an angle \( \theta \) is the reciprocal of the tangent, \( \cot(\theta) = \frac{1}{\tan(\theta)} \).
4. Evaluate \( \cot(\frac{\pi}{6}) \): Since \( \tan(\frac{\pi}{6}) = \frac{1}{\sqrt{3}} \), the cotangent is \( \cot(\frac{\pi}{6}) = \sqrt{3} \).
5. Consider the sign in the fourth quadrant: In the fourth quadrant, the cotangent is negative, so \( \cot(\frac{11\pi}{6}) = -\sqrt{3} \).