Find sin (A-B) if sin A = 4/5 with A between 90 and 180 and if cos B = 3/5 with B between 0 and 90

sin (A-B) = 24/25

Step-by-step explanation:

The trig identity for the differnce of angles tells you ...

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

We are given that sin (A) = 4/5 in quadrant II, so cos (A) = - √ (1 - (4/5) ^2) = - 3/5.

And we are given that cos (B) = 3/5 in quadrant I, so sin (B) = 4/5.

Then ...

sin (A-B) = (4/5) (3/5) - (4/5) (-3/5) = 12/25 + 12/25 = 24/25

The desired sine is 24/25.