Question #400f1

1 Answer
Nghi N.
Mar 6, 2017

# sqrt(2 - sqrt3)/2#

Explanation:

Use unit circle, trig table , and property of complement arcs.
#sin ((11pi)/12) = sin (-pi/12 + pi) = sin (pi/12)#
Evaluate #sin (pi/12)# by using trig identity:
#2sin^2 a = 1 - cos 2a#.
In this case,
#2sin^2 (pi/12) = 1 - cos (pi/6) = 1 - sqrt3/2 = (2 - sqrt3)/2#
#sin^2 (pi/12) = (2 - sqrt3)/4#
#sin (pi/12) = +- sqrt(2 - sqrt3)/2#.
Sine #sin (pi/12)# is positive, take the positive value.
Finally, #sin ((11pi)/12) = sin (pi/12) = sqrt(2 - sqrt3)/2#

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