Answer:
63/65
Step-by-step explanation:
Recall that sin(a-b) = sin(a)cos(b) - cos(a)sin(b)
Therefore, we have:
sin(a-b) = sin(a)cos(b) - (-3/5)(5/13)
sin(a-b) = sin(a)cos(b) + 3/13
Since sin(x) = opposite/hypotenuse and cos(x) = adjacent/hypotenuse, then if cos(a) = -3/5, sin(a) = 4/5. Likewise, if sin(b) = 5/13, then cos(b) = 12/13.
Therefore, sin(a-b) = (4/5)(12/13) + 3/13 = 48/65 + 3/13 = 48/65 + 15/65 = 63/65
