Question

I need help finding the exact value of sin (a + b), given that sin a =3/5 and sin b = 5/13, with a in quad 2 and b in quad 1.

Answer 1

sketch triangles in quad 2 and quad 1 for the given info

if sin a = 3/5 in II
cos a = -4/5

if sin b = 5/13 in I
cos b = 12/13

sin(a+b) = sina cosb + cosa sinb
= (3/5)(12/13) + (-4/5)(5/13)
= (36 - 20)/65 = 16/65