SOLUTION: Given cosA=1/3,A is quadrant IV and cosB=-squareroot7/4: B is in quadrant II find cos(A-B)

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Question 916121: Given cosA=1/3,A is quadrant IV and cosB=-squareroot7/4: B is in quadrant II find cos(A-B)
Answer by lwsshak3(11628) About Me  (Show Source):
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Given cosA=1/3,A is quadrant IV and cosB=-squareroot7/4: B is in quadrant II find cos(A-B)
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sinA=-√(1-cos^2A)=-√(1-1/9)=-√(8/9)=-√8/3
sinB=√(1-cos^2B)=√(1-7/16)=√(9/16)=3/4
..
cos(A-B)
=cosAcosB+sinAsinB
=1/3*-√7/4+(-√8/3)*3/4
=-√7/12-3√8/12
=-(√7+3√8)/12
..
Check:
cosA=1/3
A=289.47˚
cosB=-√7/4
B=131.41˚
A-B=289.47-131.41=158.06
cos(A-B)=cos(158.06˚)=-0.9276...
as calculated:cos(A-B)=-(√7+3√8)/12=-0.9276...