assume that 0<x<pi/2 and 0<y<pi/2. find the exact value of sin(x+y) if cosx=8/17 and siny= 12/37

621 / 629

Step-by-step explanation:

We are given the following information -

cos x = , and sin y =

Respectively we can use the following information -

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

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 ) "

Respectively cos y should be 35 / 37 -

Thus,

sin( x + y ) = ( 15 / 17 ) * ( 35 / 37 ) + ( 12 / 37 ) * ( 8 / 17 ),

sin( x + y ) = 621 / 629

Hope that helps!

d

gimmee one of those gold crowns!

~coco