Question

Given: cos a = -3/5, sin b = 5/13, and a and b are second-quadrant angles; find sin(a - b).

63/65
-33/65
33/65

Answer 1

63/65

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