Answer:
- [tex]\sqrt{3}[/tex]
Step-by-step explanation:
Using the trigonometric identity
cot x = [tex]\frac{1}{tanx}[/tex]
Thus
tan( [tex]\frac{11\pi }{6}[/tex]) = - tan ([tex]\frac{\pi }{6}[/tex])
Since [tex]\frac{11\pi }{6}[/tex] is in the fourth quadrant where tan < 0
and
2π - [tex]\frac{11\pi }{6}[/tex] = [tex]\frac{\pi }{6}[/tex] ← related acute angle
Then
- tan([tex]\frac{\pi }{6}[/tex]) = - [tex]\frac{1}{\sqrt{3} }[/tex], hence
cot ([tex]\frac{11\pi }{6}[/tex]) = [tex]\frac{1}{\frac{1}{-\sqrt{3} } }[/tex] = - [tex]\sqrt{3}[/tex]
