if cosA = 4/5; sin < 0; cosB = 12/13; 0<B<90, determine sin(A-B)

This is only barely a calculation problem. You should be sufficiently familiar with the definitions to pull this off.

You need the Pythagorean Throrem.

cos(A) = 4/5; sin < 0 ==> sin(A) = -3/5 Note that this is Quadrant IV

cos(B) = 12/13; 0<B<90 ==> sin(B) = 5/13

You need the identity:

sin(A-B) = sin(A)cos(B)-cos(A)sin(B)

Let's see what you get.