Question

Find the cotangent of the real number

Answer 1

Answer:

- $\sqrt{3}$

Step-by-step explanation:

Using the trigonometric identity

cot x = $\frac{1}{tanx}$

Thus

tan( $\frac{11\pi }{6}$) = - tan ($\frac{\pi }{6}$)

Since $\frac{11\pi }{6}$ is in the fourth quadrant where tan < 0

and

2π - $\frac{11\pi }{6}$ = $\frac{\pi }{6}$ ← related acute angle

Then

- tan($\frac{\pi }{6}$) = - $\frac{1}{\sqrt{3} }$, hence

cot ($\frac{11\pi }{6}$) = $\frac{1}{\frac{1}{-\sqrt{3} } }$ = - $\sqrt{3}$