You are given that sin(A)=35, with A in Quadrant I, and cos(B)=−725, with B in Quadrant III. Find cos(A−B). Give your answer as a fraction.

Answer 1

I assume that you meant to write sin(A) = 3/5 in quadrant 1 and cos(B) = -7/25 in Quadrant 3

Note Pythagorean triples 3-4-5 and 7-24-25

In Quadrant 3, sin is negative, so sin = -24/25

In Quadrant 1, cos is positive, so cos = 4/5

cos(A-B) = cosAcosB + sinAsinB = 4/5(-7/25) + 3/5(-24/25) = -100/125 = -4/5