SOLUTION: Can you help me please ;Given; sin (x+y) = sin x cos y + cos x sin y and cos (× + y)= cos x cos y - sin x sin y. If sin x = 0,8 and sin y= 0,6 , calculate sin ( x + y )

Algebra.Com
Question 984820: Can you help me please ;Given; sin (x+y) = sin x cos y + cos x sin y and cos (× + y)= cos x cos y - sin x sin y. If sin x = 0,8 and sin y= 0,6 , calculate sin ( x + y )
Found 2 solutions by Boreal, solver91311:
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
to do this we need cos x and cos y
sin^2x+cos^2x=1
.64 +cos^2= 1
cos^2x =0.36; cos x=0.6
In the same way sin y=0.6; cos y=0.8
;;
sin (x+y)=0.64+0.36=1
x=53.1 deg
y=36.9 deg
sin 90=1
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!

First, even though  and  are given, we still need to know  and  in order to calculate 

If we know that , then we can determine the value of cosine by the following process:

Given:                  
Square both sides:      
Apply the Pythagorean
  Identity              
A little algebra        
Take the root           

Since your problem does not restrict the value of  or  to a specific quadrant, the value of cosine, when calculated on the basis of the value of sine, is ambiguous.  We should look out for more than one solution to your problem.






Now we have all the information required to perform the needed calculation.



So

or

Hence

or

John

My calculator said it, I believe it, that settles it
RELATED QUESTIONS

Can you help me please; Given sin (x+y) = sin x cos y + cos x sin y and cos (x+y) =... (answered by Alan3354)
Can you help battle with this; Given ; sin(x+y) = sin x cos y +cos x sin y and cos... (answered by Alan3354)
Verify the identity. (cos(x) - cos(y))/(sin(x) + sin(y)) + (sin(x) - sin(y))/(cos(x) + (answered by solver91311)
Simplify cos(x)cos(y) +... (answered by Edwin McCravy)
Given sin (x+y)= sin x cos y + cos x sin y and cos(x+y) = cos x cos y -sin x sin y... (answered by Alan3354)
If sin (x+y)=0.9 and sin(x-y)=0.6, determine (sin x)(cos... (answered by lwsshak3)
If sin (x+y)=0.9 and sin(x-y)=0.6, determine (sin x)(cos... (answered by tommyt3rd)
Given sin (x+y)= sin x cos y + cos x sin y and cos(x+y) = cos x cos y - sin x sin y... (answered by Alan3354)
Will you please help me with this equation: Given: sin (x+y)=sin x cos y + cos x sin y... (answered by jim_thompson5910)