SOLUTION: suppose sin(x) = 3/5 with x in quadrant I, and cos(y) = 12/13 with y in quadrant IV. find the exact value of cos (x-y)

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Question 796418: suppose sin(x) = 3/5 with x in quadrant I, and cos(y) = 12/13 with y in quadrant IV. find the exact value of cos (x-y)
Answer by lwsshak3(11628) About Me  (Show Source):
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suppose sin(x) = 3/5 with x in quadrant I, and cos(y) = 12/13 with y in quadrant IV. find the exact value of cos (x-y)
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Identity:sin(x-y)=sin(x)cos(y)-cos(x)sin(y)
..
sin(x)=3/5
working with a 3-4-5 reference right triangle in quadrant I where sin and cos>0
cos(x)=4/5
..
cos(y)=12/13
working with 5/12/13 reference right triangle in quadrant IV where sin<0 and cos>0
sin(y)=-5/13
..
sin(x)cos(y)-cos(x)sin(y)
=(3/5)*(12/13)-(4/5)*(-5/13)
=(36/65)+(20/65)=56/65
sin(x+y)=56/65
..
Check:(with calculator)
sin(x)=3/5
x≈36.87 deg
cos(y)=12/13
y≈337.38 deg (in quadrant IV)
x-y≈-300.51 deg
sin(x-y)=sin(-300.51)deg≈0.8615..
exact ans as calculated=56/65≈0.8615..