Question

How do you find sin(-105degrees) using the half angle formula?

Answer 1

Find sin (-105)

Answer: `sin -105 = +- sqrt(2 + sqrt3)/2`

Explanation:

Call sin (-105) = sin t --> cos (-210) = cos (2t)
On the trig unit circle,
`cos 2t = cos (-210) = cos (-30 - 180) = - cos 30 = (-sqrt3)/2`
Apply the trig identity: `cos 2t = 1 - sin^2 t:`

`cos 2t = (-sqrt3)/2 = 1 - 2sin^2 t`
`2sin^2t = 1 + (sqrt3/2) = (2 + sqrt3)/2`
sin^t = (2 + sqrt3)/4

`sin t = sin (-105) = +- sqrt(2 + sqrt3)/2`