Find the exact value of cos uv 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 = 5/13, with v in quadrant I.

cos (u+v) =

(simplify your answer. Type an integer or a simplified fraction)

Solution

sin u = -3/5 , with u in quadrant III, and sin v = 5/13, with v in quadrant I.

cosu = - 4/5 ; cosv = 12/13

Now , cos(u +v) = cosucosv - sinusinv

= (-4/5)(12/13) - (-3/5)(5/13)

= (-48+15)/65

= - 33/65