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
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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...