Solve this problem please

Question

Given that sin u = −2/5 , u in quadrant III, and cos v = 3/4 , v in quadrant IV, find the exact value of sin(u + v).

Answer 1

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

Need cos(u) and sin(v) taking into consideration the signs depending on quadrants

cos(u) = -√(25-4)/5 = -√21/5

sin(v) = √(16-9)/4

Then just substitute values of the sines and cosines into the sine angle addition equation above.