Question

How do you simplify using the sum and difference formula `sin((11pi)/12)`?

Answer 1

sin (pi/12)

Explanation:

`sin ((11pi)/12) = sin (-pi/12 + sin ((12pi)/12)) = sin (-pi/12 + pi) = sin (pi/12)`

NOTE. We can evaluate sin (pi/12) by the identity
`cos (pi/6) = sqrt3/2 = 1 - 2sin^2 (pi/12).`
`sin^2 (pi/12) = (2 - sqrt3)/4`
`sin (pi)/12 = + sqrt(2 -sqrt3)/2` --> (sin (pi/12) is positive.