Question

evaluate. write your answer in simplified, rationalized form. do not round.

$$ cot left( \frac { pi } { 6 } ight) = $$

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:

\(\sqrt{3}\)