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 ->  Trigonometry-basics -> 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 )       Log On


   

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) About Me  (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) About Me  (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