Answer:
The value of sin(ø + φ) can be found using the formula:
sin(ø + φ) = sin ø cos φ + cos ø sin φ
First, we need to find the values of cos ø and cos φ:
cos ø = √(1 - sin² ø) = √(1 - (-5/13)²) = √(1 - 25/169) = √(144/169) = 12/13
cos φ = √(1 - tan² φ) = √(1 - (-8/15)²) = √(1 - 64/225) = √(161/225) = 9/15
Next, we find the values of sin φ:
sin φ = √(1 - cos² φ) = √(1 - (9/15)²) = √(1 - 81/225) = √(144/225) = 12/15
Finally, we can substitute these values into the formula and simplify:
sin(ø + φ) = sin ø cos φ + cos ø sin φ
= -5/13 * 9/15 + 12/13 * 12/15
= -45/195 + 144/195
= 99/195
Therefore, the value of sin(ø + φ) is 99/195, which is approximately equal to option 3: 171/221.