SOLUTION: If x is in the first and y is in the second quadrant, sin = 24/25, and sin y = 4/5, find the exact value of sin (x+y), cos(x-y). tan (x-y). I have sin(x+y) = (sinx)(cosy) + (cosx)

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Question 756722: If x is in the first and y is in the second quadrant, sin = 24/25, and sin y = 4/5, find the exact value of sin (x+y), cos(x-y). tan (x-y). I have sin(x+y) = (sinx)(cosy) + (cosx)(siny) = (24/25)(cosy) + (cosx)(4/5). Am I going about this the correct way? Then I figured (not sure if correct) cos y = -3/5 and cos x = 7/25. Putting that all into the equation I get (-72/125)+ (28/125) = Sin (x+y)
= Sin (24/25+ 4/5) =
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
x is in the first and y is in the second quadrant, sin = 24/25, and sin y = 4/5, find the exact value of sin (x+y), cos(x-y). tan (x-y). I have sin(x+y) = (sinx)(cosy) + (cosx)(siny) = (24/25)(cosy) + (cosx)(4/5). Am I going about this the correct way? Then I figured (not sure if correct) cos y = -3/5 and cos x = 7/25. Putting that all into the equation I get (-72/125)+ (28/125) = Sin (x+y) = 
That is correct: sin(x+y) = (-72/125)+(28/125) = = -44/125  

However this expression is wrong:

= Sin (24/25+ 4/5) = 
The 24/25 and the 4/5 are sines, not angles, and writing the above is
incorrect because that looks like "the sine of the sum of two sines",
"not the sum of two angles".

Correct final answers:  

sin(x+y) = -44/125
cos(x-y) = 3/5
tan(x-y) = -4/3

Edwin
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