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