Question

If sin x= 3/5 , cos y = -12/13 . Find value sin (x+y)

Answer 1

Answer:

-56/65  or  -16/65

Step-by-step explanation:

    sin ( x + y ) = sin x cos y + cos x sin y

so we just need to work out cos x and sin y, too.

From cos² x + sin² x = 1 we get

 cos x = ±√( 1 - sin² x ) = ±√( 1 - 9/25 ) = ±√( 16/25 ) = ±4/5

Similarly,

 sin y = ±√( 1 - cos² y ) = ±√( 1 - 144/169 ) = ±√( 25/169 ) = ±5/13

So

sin ( x + y ) = sin x cos y + cos x sin y

= (3/5) × (-12/13) + (±4/5) × (±5/13)

= -36/65 ± 20/65

= -56/65  or  -16/65

Hope that helps!

Answer 2

Step-by-step explanation:

sinx = 3/5

cosx= 4/5

( by pythagorus theorem)

cosy = -12/13

siny = 5/13

sin(x+y) = sinxcosy+cosxsiny

=3/5*-12/13 + 4/5*5/13

= -36/65 + 20/65

= -16/65