Find the exact value for

Question

sin (x+y) given sin x = 8/17 for x in quadrant 2 and cos y= 6/7 for y in quadrant 4

Answer 1

sin (x+y) = sinx cosy + cos x sin y 

 

sin x = 8/17

 

so cos x =- 15/17

 

cos y = 6/7

 

so sin y =- sqrt 13/7 =- 3.6 /7

 

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

 

              = (8/17)(6/7) + (-15/17)(-3.6/7)

 

              = 48/119 + 54/119

    

 

             =102/119 =6/7