Question

How do you use the angle sum identity to find the exact value of cos 285?

Answer 1

Use the trig unit circle as proof.

`cos 285 = cos (180 + 105) = cos (90 - 15) = sin 15`

`sin 15 = sin (60 - 45) = sin 60.cos 45 - sin 45.cos 60` =

cos 285 = `sin 15 = (sqrt3/2)(sqrt2/2) - (sqrt2/2)(1/2) = (sqrt6 - sqrt2)/4`