Answer:
621 / 629
Step-by-step explanation:
We are given the following information -
cos x = [tex]\frac{8}{17}[/tex], and sin y = [tex]\frac{12}{37}[/tex]
Respectively we can use the following information -
sin( x + y ) = sin x ( cos y ) + sin y ( cos x ),
[tex]cos^2x + sin^2x = 1,\\cos^2y + sin^2y = 1[/tex]
Knowing that cos^2x + sin^2x = 1, cos^2y + sin^2y = 1, we can calculate the value of sin x and cos y, plugging it into the first bit " sin( x + y ) = sin x ( cos y ) + sin y ( cos x ) "
[tex]sin^2x = 1 - cos^2x,\\sin^2x = 1 - ( 8 / 17 )^2,\\sin^2x = 15^2 / 17^2\\----------------\\sin ( x ) = 15 / 17[/tex]
Respectively cos y should be 35 / 37 -
[tex]cos^2y = 1 - sin^2y,\\cos^2y = 1 - ( 12 / 37 )^2,\\cos^2y = 35^2 / 37^2\\----------------\\cos ( y ) = 35 / 37[/tex]
Thus,
sin( x + y ) = ( 15 / 17 ) * ( 35 / 37 ) + ( 12 / 37 ) * ( 8 / 17 ),
sin( x + y ) = 621 / 629
Hope that helps!
