Question

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

Answer: sqrt6-sqrt2/4

Thanks

Answer 1

You might notice that 225 = 180 + 75
so sin 255 = sin(180+75)
= sin 180cos 75 + cos180sin75
= -sin75

now 75 = 45 + 30
so sin(75) = sin(45+30)
= sin45cos30 + cos45sin30
= (1/√2)(√3/2) + (1/√2)(1/2) or
= (√2/2)(√3/2) + )√2/2)(1/2)
= (√6 + √2)/4

so sin 255 = -(√6 + √2)/4