Find the exact value of cosu v given that sin u 35 with u

Find the exact value of cos(u + v) given that sin u = -3/5, with u in quadrant III, and sin v = 12/13, with v in the quadrant II. cos (u + v) = (Simplify your answer. Type an integer or a simplified fraction.)

Solution

sin u = -3/5

cos u = - 4/5

sin v = 12/13

cos v = - 5/13

cos ( u + v) = cos u cos v - sin u sin v

plugging the values

cos ( u + v ) = ( -4/5)(-5/13) - ( -3/5 )(12/13)

= 20/65 + 36/65

= 56/65

cos ( u + v) = 56 / 65