Question 746467
Given: A lies in Quadrant III and B lies in Quadrant II,
m1212.
Find the exact value of cos(A - B). SinA= -8/17 CosB= -4/5
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sinA=-8/17
{{{cos(A)=sqrt(1-sin^2(A))=sqrt(1-64/289)=sqrt(225/289)=-15/17}}}
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cosB= -4/5
sinB=3/5 (from 3-4-5 right triangle)
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cos(A-B)=cosAcosB+sinAsinB=(-15/17)(-4/5)+(-8/17)(3/5)=60/85-24/85=36/85
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Check: (with calculator)
sinA=-8/17
A≈208.07º
cosB=-4/5
B≈143.13º
A-B≈64.94º
cos(A-B)≈cos(64.94º)≈0.4235..
Exact ans=36/85≈0.4235..