evaluate. write your answer in simplified, rationalized form. do not round. \n\n$$ cot left( \frac { pi } {…

Explanation:

Step1: Use the cotangent formula

We know that (\cot\theta=\frac{\cos\theta}{\sin\theta}). For (\theta = \frac{\pi}{6}), (\cos(\frac{\pi}{6})=\frac{\sqrt{3}}{2}) and (\sin(\frac{\pi}{6})=\frac{1}{2}). So, (\cot(\frac{\pi}{6})=\frac{\cos(\frac{\pi}{6})}{\sin(\frac{\pi}{6})}).

Step2: Substitute the values

Substitute (\cos(\frac{\pi}{6})=\frac{\sqrt{3}}{2}) and (\sin(\frac{\pi}{6})=\frac{1}{2}) into the formula: (\cot(\frac{\pi}{6})=\frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}). When dividing by a fraction, we multiply by its reciprocal. So (\frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}=\frac{\sqrt{3}}{2}\times\frac{2}{1}). The (2)s cancel out.

Answer:

(\sqrt{3})