is this correct?

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

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

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

255 i guess that makes the first 1 wrong.

sin 255 should be

-(1/4)[sqrt6 + sqrt2]

Yes, the result is correct. Here's a step-by-step explanation of how to calculate it:

1. Start with the given angle, 255 degrees.
2. Rewrite 255 as the sum of 180 and 75: 255 = 180 + 75.
3. Use the sum formula for sine: sin(A + B) = sin(A)cos(B) + cos(A)sin(B).
4. Substitute the values into the formula: sin(225) = sin(180 + 45) = sin(180)cos(45) + cos(180)sin(45).
5. Evaluate the trigonometric functions at those angles:
- sin(180) = 0 (sine of 180 degrees is zero).
- cos(45) = sqrt(2)/2 (cosine of 45 degrees is square root of 2 divided by 2).
- cos(180) = -1 (cosine of 180 degrees is -1).
- sin(45) = sqrt(2)/2 (sine of 45 degrees is square root of 2 divided by 2).
6. Perform the calculations: sin(225) = 0 + (-1)(sqrt2/2).
7. Simplify the expression: sin(225) = -(sqrt2)/2.

Therefore, the correct value for sin 255 degrees is -(sqrt2)/2.