Question

How do you find the value of `sin(-(11pi)/12)`?

Answer 1

`- sqrt(2 - sqrt3)/2`

Explanation:

Trig table and unit circle -->
`sin ((-11pi)/12) = sin (pi/12 - (12pi)/12) = sin (pi/12 - pi) = - sin (pi/12)`
Evaluate `sin (pi/12)` by using trig identity:
`2sin^2 a = 1 - cos 2a`
`2sin^2 (pi/12) = 1 - cos (pi/6) = 1 - sqrt3/2 = (2 - sqrt3)/2`
`sin^2 (pi/12) = (2 - sqrt3)/4`
`sin (t/12) = +- sqrt(2 - sqrt3)/2`
Because sin (pi/12) is positive, take the positive answer.
Finally,
`sin ((-11pi)/12) = - sin (pi/12) = - sqrt(2 - sqrt3)/2`