Question

How do I find the value of cot 5pi / 6?

Answer 1

Find `cot ((5pi)/6)`

Ans: `- sqrt3`

Explanation:

On the trig unit circle,
`cot ((5pi)/6) = cot (-pi/6 + pi) = - cot (pi/6)`
Trig Table of Special Arcs gives -->
`cot (pi/6) = sqrt3`, then,
`cot ((5pi)/6) = -cot (pi/6) = - sqrt3`

Answer 2

`-sqrt3`

Explanation:

`cot((5pi)/6)=cos((5pi)/6)/sin((5pi)/6)`

Note that `(5pi)/6` has a reference of angle of `pi/6` and is in Quadrant `"II"`.

Thus, cosine will be negative and sine will be positive.

`cos(pi/6)=sqrt3/2`

`cos((5pi)/6)=-sqrt3/2`

`sin(pi/6)=1/2`

`sin((5pi)/6)=1/2`

Thus,

`cot((5pi)/6)=(-sqrt3/2)/(1/2)=-sqrt3/2(2/1)=-sqrt3`