Question

How do you use the half-angle identity to find the exact value of sin (-pi/12)?

Answer 1

Find `sin (-pi/12)`
Answer: - 0.259

Explanation:

Call`sin (-pi/12) = sin t -> cos 2t = cos (- pi/6) = cos (pi/6) = sqrt3/2`
Use trig identity: `cos 2t = sqrt3/2 = 1 - 2sin^2 t`
`2sin^2 t = (2 - sqrt3)/2`
`sin^2 t = (2 -sqrt3)/4`

`sin t = sin (-pi/12) = +- sqrt(2 - sqrt3)/2` = +- 0.259.
Only the negative answer is accepted: - 0.259