Question

Use a sum or difference identity to find exact value of sin 255.

Answer 1

sin (x + y) = sin x cos y + cos x sin y

sin 255
= sin (210 + 45)
= sin 210 cos 45 + cos 210 sin 45
= (-1/2)(√(2)/2) + (-√(3)/2)(√(2)/2)
= -√(2)/4 + (-√(6)/4)
= -√(2)/4 - √(6)/4
= (-√(2) - √(6)) / 4