How do you evaluate #cos((11pi) / 12)#?

1 Answer
Mar 20, 2016

#sqrt(2 + sqrt3)/2#

Explanation:

On the trig unit circle,
#cos((11pi)/12) = cos (pi/12#).
Evaluate #cos (pi/12)# bu applying the identity:
#cos 2a = 2cos^2 a - 1#
#cos (pi/6) = sqrt3/2 = 2cos^2 (pi/12) - 1#
#2cos^2 (pi/12) = 1 + sqrt3/2 = (2 + sqrt3)/2#
#cos^2 (pi/12) = (2 + sqrt3)/4#
#cos (pi/12) = sqrt(2 + sqrt3)/2# (#cos (pi/12)# is positive)