Question

How do you use a half-angle formula to simplify `sin -105`?

Answer 1

sin -105 = - sin 105

`cos 210 = cos (30 + 180) = - cos 30 = -(sqrt3)/2`

`2sin^2 105 = 1 - cos 210 = 1 + 0.866 = 1.866`

`sin^2 105 = 1.866/2 = 0.933 -> sin x = +- 0.97`

sin -105 = - 0.97