Question

Find the value of the following:

sin (-105°)

Answer 1

sin (-105°) = -sin (105°) (∵ sin (-θ) = – sin θ)

= -[sin(60° + 45°)]

= -[sin 60° cos 45° + cos 60° sin 45°]

`= -[sqrt3/2 xx 1/sqrt2 + 1/2 xx 1/sqrt2]`

`= - [sqrt3/(2sqrt2) + 1/(2sqrt2)]`

`= - [(sqrt3 + 1)/(2sqrt2)]`