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

2 Answers
Oct 25, 2015

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#

Jan 8, 2016

#-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#