Find the exact value of the trigonometic function at the given real number of cot(5pi/3)

Answer 1

5π/3 is in quadrant IV
in IV the cotanglent like the tangent is negative.
the "related" angle is π/3 ......(5π/3 radians = 300°, π/3 radians = 60° )

so cot 5π/3
= -cot π/3

we know tan π/3 = √3/1 , so

-cot π/3 = -1/√3