SOLUTION: Suppose sin x = 5/7
cos x > 0, sin y = − 1/5
and cos y < 0. Then
cos x =
cos y =
Find each of the following quantities:
sin(x + y) =
cos(x + y) =
tan(x + y) =
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-> SOLUTION: Suppose sin x = 5/7
cos x > 0, sin y = − 1/5
and cos y < 0. Then
cos x =
cos y =
Find each of the following quantities:
sin(x + y) =
cos(x + y) =
tan(x + y) =
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Question 924704: Suppose sin x = 5/7
cos x > 0, sin y = − 1/5
and cos y < 0. Then
cos x =
cos y =
Find each of the following quantities:
sin(x + y) =
cos(x + y) =
tan(x + y) =
Thank you Answer by lwsshak3(11628) (Show Source):
You can put this solution on YOUR website! Suppose sin x = 5/7
cos x > 0, sin y = − 1/5
and cos y < 0. Then
cos x =
cos y =
Find each of the following quantities:
sin(x + y) =
cos(x + y) =
tan(x + y) =
***
sinx=5/7
cosx>0
reference angle x is in quadrant I where sin>0, cos>0
cosx=√(1-sin^2(x))=√(1-25/49)=√(24/49)=√24/7
..
siny=-1/5
cosy<0
reference angle y is in quadrant III where sin<0, cos<0
cosy=-√(1-sin^2(y))=-√(1-1/25)=-√(24/25)=-√24/5
..
sin(x+y)=sinxcosy+cosxsiny=5/7*-√24/5+√24/7*-1/5=-5√24/35+-√24/35=-6√24/35
cos(x+y)=cosxcosy-sinxsiny=√24/7*-√24/5-5/7*-1/5=-24/35+5/35=-19/35
tan(x+y)=sin(x+y)/cos(x+y)=-6√24/-19=6√24/19
..
Check:
sinx=5/7
x=45.5847˚
siny=1/5
y=191.537
x+y=237.12˚
..
sin(x+y)=sin(237.12)≈-0.8398 (w/calculator)
exact value as computed=-6√24/35≈-0.8398
..
cos(x+y)=cos(237.12)≈-0.5429(w/calculator)
exact value as computed=-19/35≈-0.5429
..
tan(x+y)=tan(237.12)≈1.5469(w/calculator)
exact value as computed=6√24/19≈1.5470
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