is this correct?

Question

sin 255degrees
225 = 180 + 45
sin(225) = sin(180 + 45) = sin(180)cos(45) + cos(180)sin(45)
sin(225) = 0 + (-1)(sqrt2/2)
sin(225) = -(sqrt2)/2

Answer 1

or

sin (255°) = sin (180° + 75°)

= - sin 75° [The terminal side of the angle lies in quadrant III, so the sine function is negative.]

= - sin (45° + 30°)

= - (sin 45°cos 30° + cos 45°sin 30°) [Use sin (A + B) = sin A cos B + cos A sin B.]

= - [( Square root of (2) /2)( Square root of (3) /2) + ( Square root of (2) /2)(1/2)]

= - ( Square root of (6) + Square root of (2) /4) = - Square root of (6) - Square root of (2) /4

Answer 2

Your first two lines make it unclear whether you want sin 255 or sin 225.

Answer 3

255 i guess that makes the first 1 wrong.

Answer 4

sin 255 should be
-(1/4)[sqrt6 + sqrt2]