Question

Find each value if sin A = 12/13 with 90 degrees <= A <= 270 degrees and if sin B = -7/25 with -90 degrees <= B <= 90 degrees.

sin(A - B)

sin(A + B)

Answer 1

if sinA = 12/13, and since the since is +
A must be in II
using our standard 5-12-13 triangle,
cosA = -5/13

if sinB = -7/25,
to state -90 ≤ B ≤ 90 is ambiguous, since you could be on the right or the left of the y-axis
I will assume B is in III , (could be in IV)
then using our standard 7-24-25 right-angled triangle, we can say that
cosB = -24/25

ok, now

sin(a-b) = sinAcosB - cosAsinB
= (12/13)(-24/25) - (-5/13)(-7/25)
= (-288/325 - 35/325) = -323/325

Using the expansion for sin(A+B) , I will let you do the other one