SOLUTION: find the exact value of the expression using the provided information find sin (A-B) given that cos A= 1/3 with A in quadrant I and sin B = -1/2 with B in quadrant IV

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Question 767510: find the exact value of the expression using the provided information
find sin (A-B) given that cos A= 1/3 with A in quadrant I and sin B = -1/2 with B in quadrant IV
Found 2 solutions by stanbon, lwsshak3:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
find the exact value of the expression using the provided information
find sin (A-B) given that cos A= 1/3 with A in quadrant I and sin B = -1/2 with B in quadrant IV
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cos A= 1/3 with A in quadrant I
sin A = sqrt(3^2-1^2)/3 = sqrt(8)/3 = (2/3)sqrt(2)
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sin B = -1/2 with B in quadrant IV
cos B = sqrt(2^2-1^2)/2 = sqrt(3)/2
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sin(A-B) = sinAcosB - cosAsinB
= [(2/3)sqrt(2)*sqrt(3)/2) - (1/3)(-1/2)
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= (1/3)sqrt(6) + 1/6
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Cheers,
Stan H.
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Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
find the exact value of the expression using the provided information
find sin (A-B) given that cos A= 1/3 with A in quadrant I and sin B = -1/2 with B in quadrant IV
***
sin(A-B)=sinAcosB-cosAsinB
sinA=√(1-cos^2A)=√(1-1/9)=√(8/9)=√8/3
cosB=√(1-sin^2B)=√(1-1/4)=√(3/4)=√3/2
sin(A-B)=sinAcosB-cosAsinB=(√8/3*√3/2)-(1/3*-1/2)=√24/6+1/6=(√24+1)/6
Check with calculator:
cosA=1/3
A=70.53º
sinB=-1/2
B=330º
A-B=70.53-330=-259.47
sin(A-B)=sin(-259.47)≈0.9831...(In quadrant II where sin>0)
exact value=(√24+1)/6≈0.9831...