document.write( "Question 811262: Given cos(x) = 1⁄2 with 0o < x < 90o, and cos(y) = 1⁄7 with 270o < y < 360o. Find cos(x + y). \n" ); document.write( "

Algebra.Com's Answer #488685 by lwsshak3(11628) $\"\"$ $\"About$

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Given cos(x) = 1⁄2 with 0o < x < 90o, and cos(y) = 1⁄7 with 270o < y < 360o. Find exact value of cos(x + y).
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\n" ); document.write( "cos(x)=1/2(Q1)
\n" ); document.write( "sin(x)=√(1-cos^(x))=√(1-1/4)=√(3/4)=√3/2
\n" ); document.write( "cos(y)=1/7(Q4)
\n" ); document.write( "sin(y)=-√(1-cos^(y))=-√(1-1/49)=-√(48/49)=-√48/7=-4√3/7
\n" ); document.write( "cos(x+y)=cos(x)cos(y)-sin(x)sin)y)
\n" ); document.write( "=(1/2)*(1/7)+√3/2*4√3/7
\n" ); document.write( "=1/14+12/14=13/14
\n" ); document.write( "..
\n" ); document.write( "Check:(w/calculator)
\n" ); document.write( "cos(x)=1/2
\n" ); document.write( "x=60˚
\n" ); document.write( "cos(y)=1/7
\n" ); document.write( "y≈278.21˚
\n" ); document.write( "x+y≈338.21˚
\n" ); document.write( "..
\n" ); document.write( "cos(x+y)≈cos(338.21˚)≈0.9285..
\n" ); document.write( "exact value=13/14≈0.9285.. \n" ); document.write( "

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