How do I find the value of cos 11pi / 6?

1 Answer
Aug 14, 2015

Find #cos ((11pi)/6)#

Ans: #sqrt3/2#

Explanation:

Cal #cos ((11pi)/6) = cos t#

#cos 2t = cos ((22pi)/6) = cos ((-2pi)/6 + 12(2pi))# =
#= cos (-pi/3) = cos (pi/3) = 1/2#
Use trig identity: #cos 2t = 2cos^2 t - 1#

#2cos^2 t = 1 + 1/2 = 3/2#
#cos^2 t = 3/4 #
#cos ((11pi)/6) = cos t = +- sqrt3/2#
Since the arc (11pi)/6 is located in Quadrant IV, only the positive answer is accepted.
#cos ((11pi)/6) = sqrt3/2#