Question

What is the exact value of cot(5(pi)/6)?

Answer 1

cot(5π/6)
= cos(5π/6) / sin(5π/6)
= sin(π/2 - 5π/6)/ cos(π/2 - 5π/6)
= sin(-π/3)/cos(-π/3)
= -sin(π/3)/cos(π/3)
= -(sqrt(3)/2)/(1/2)
= -sqrt(3)

Answer 2

Use Google, if you don't have a calculator. Type
tan(5*pi/6) =
in the search box.
Then take the reciprocal of that answer, for the cotangtent.
You may recognize the answer as the square root of 3.

5 pi/6 is a 150 degree angle. The reference angle is 30 degrees, but cosine is negative in the second quadrant.