evaluate: $cotleft(\frac{pi}{3}\right)$\n$\frac{2sqrt{3}}{3}$\n$sqrt{2}$\n$2$\n$\frac{sqrt{3}}{3}$

Explanation:

Step1: Recall cotangent definition

$\cot(x)=\frac{\cos(x)}{\sin(x)}$

Step2: Find $\cos(\frac{\pi}{3})$ and $\sin(\frac{\pi}{3})$

We know that $\cos(\frac{\pi}{3})=\frac{1}{2}$ and $\sin(\frac{\pi}{3})=\frac{\sqrt{3}}{2}$

Step3: Calculate $\cot(\frac{\pi}{3})$

$\cot(\frac{\pi}{3})=\frac{\cos(\frac{\pi}{3})}{\sin(\frac{\pi}{3})}=\frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}}=\frac{1}{\sqrt{3}}=\frac{\sqrt{3}}{3}$

Answer:

$\frac{\sqrt{3}}{3}$