Question 811262
Given cos(x) = 1&#8260;2 with 0o < x < 90o, and cos(y) = 1&#8260;7 with 270o < y < 360o. Find exact value of cos(x + y).
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cos(x)=1/2(Q1)
sin(x)=&#8730;(1-cos^(x))=&#8730;(1-1/4)=&#8730;(3/4)=&#8730;3/2
cos(y)=1/7(Q4)
sin(y)=-&#8730;(1-cos^(y))=-&#8730;(1-1/49)=-&#8730;(48/49)=-&#8730;48/7=-4&#8730;3/7
cos(x+y)=cos(x)cos(y)-sin(x)sin)y)
=(1/2)*(1/7)+&#8730;3/2*4&#8730;3/7
=1/14+12/14=13/14
..
Check:(w/calculator)
cos(x)=1/2
x=60&#730;
cos(y)=1/7
y&#8776;278.21&#730;
x+y&#8776;338.21&#730;
..
cos(x+y)&#8776;cos(338.21&#730;)&#8776;0.9285..
exact value=13/14&#8776;0.9285..