Question

Question #400f1

Answer 1

`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`