We know that sin(x)2 + cos(x)2 = 1
(3/5)2 + cos(x)2 = 1
9/25 + cos(x)2 = 25/25
cos(x)2 = 16/25
cos(x) = +/- (4/5)
Since it is in second quadrant cos(x) = -4/5
sin(y)2 + (-12/13)2 = 1
sin(y)2 + 144/169 = 169/169
sin(y)2 = 25/169
sin(y) = +/- 5/13
Since it is in second quadrant sin(y) = 5/13
sin(x) = 3/5
cos(x) = -4/5
sin(y) = 5/13
cos(y) = -12/13
sin(x + y) => sin(x)cos(y) + sin(y)cos(x)
=> (3/5) (-12/13) + (5/13) (-4/5)
=> -36 / 65 + -20 / 65
=> -56/65
So, sin(x+y) = -56/65
