Question

How do you find the exact functional value sin (-165) using the cosine sum or difference identity?

Answer 1

Find sin (-165)

Ans: `- (sqrt6 - sqrt2)/4`

Explanation:

sin (-165) = - sin (165) = - sin (45 + 120)
Trig Table -->
sin (45 + 120) = sin 45.cos 120 + sin 120.cos 45 =
`(sqrt2/2)(-1/2) + (sqrt2/2)(sqrt3/2) = (sqrt6 - sqrt2)/4`

`sin (-165) = - sin (165) = - (sqrt6 - sqrt2)/4`

Check by calculator:
sin (-165) = -0.26
`- (sqrt6 - sqrt2)/4 = 1.04/4 = 0.26`. OK