Find cos(A + B) if sin A = 3/5 and sin B = 5/13 with A is quadrant II and B in quadrant I.

Answer 1

Since A is in Quadrant 2, cosA < 0. So, cosA = -√(1 - sin²A) = -√(1 - 9/25) = -4/5.

Since B is in Quadrant 1, cosB > 0. So, cosB = √(1 - sin²B) = √(1 - 25/169) = 12/13

cos(A+B) = (cosA)(cosB) - (sinA)(sinB) = (-4/5)(12/13) - (3/5)(5/13) = -63/65