SOLUTION: find the exact value of the expression using the provided information find cos(A+B) given that cos A = -1/6 with A in quadrant III and cos B= -3/5 with B in quadrant III

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Question 767509: find the exact value of the expression using the provided information
find cos(A+B) given that cos A = -1/6 with A in quadrant III and cos B= -3/5 with B in quadrant III
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 cos(A+B) given that cos A = -1/6 with A in quadrant III and cos B= -3/5 with B in quadrant III
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cos(A+B)=cosAcosB-sinAsinB
sinA=√(1-cos^2A)=√(1-1/36)=-√35/36)=-√35/6
sinB=√(1-cos^2B)=√(1-9/25)=√16/25)=-4/5
cos(A+B)=cosAcosB-sinAsinB=(-1/6*-3/5)-(-√35/6*-4/5)=3/30-4√35/30=(-4√35+3)/30
Check with calculator:
cosA=-1/6
A≈260.4º
cosB=-3/5
B=233.1º
A+B=260.4º+233.1º≈493.5º
cos(A+B)=cos(493.5)≈-0.688...(In quadrant II where cos<0)
exact value=(-4√35+3)/30≈-0.688...