Question

Find the cotangent of the real number

Answer 1

-
`√(3)`

Explanation:

Using the trigonometric identity

cot x =
`(1)/(tanx)`

Thus

tan(
`(11\pi )/(6)`) = - tan (
`(\pi )/(6)`)

Since
`(11\pi )/(6)` is in the fourth quadrant where tan < 0

and

2π -
`(11\pi )/(6)` =
`(\pi )/(6)` ← related acute angle

Then

- tan(
`(\pi )/(6)`) = -
`(1)/(√(3) )`, hence

cot (
`(11\pi )/(6)`) =
`(1)/((1)/(-√(3) ) )` = -
`√(3)`