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Suppose sin x = 5/7
\n" ); document.write( "cos x > 0, sin y = − 1/5
\n" ); document.write( "and cos y < 0. Then
\n" ); document.write( "cos x =
\n" ); document.write( "cos y =
\n" ); document.write( "Find each of the following quantities:
\n" ); document.write( "sin(x + y) =
\n" ); document.write( "cos(x + y) =
\n" ); document.write( "tan(x + y) =
\n" ); document.write( "***
\n" ); document.write( "sinx=5/7
\n" ); document.write( "cosx>0
\n" ); document.write( "reference angle x is in quadrant I where sin>0, cos>0
\n" ); document.write( "cosx=√(1-sin^2(x))=√(1-25/49)=√(24/49)=√24/7
\n" ); document.write( "..
\n" ); document.write( "siny=-1/5
\n" ); document.write( "cosy<0
\n" ); document.write( "reference angle y is in quadrant III where sin<0, cos<0
\n" ); document.write( "cosy=-√(1-sin^2(y))=-√(1-1/25)=-√(24/25)=-√24/5
\n" ); document.write( "..
\n" ); document.write( "sin(x+y)=sinxcosy+cosxsiny=5/7*-√24/5+√24/7*-1/5=-5√24/35+-√24/35=-6√24/35
\n" ); document.write( "cos(x+y)=cosxcosy-sinxsiny=√24/7*-√24/5-5/7*-1/5=-24/35+5/35=-19/35
\n" ); document.write( "tan(x+y)=sin(x+y)/cos(x+y)=-6√24/-19=6√24/19
\n" ); document.write( "..
\n" ); document.write( "Check:
\n" ); document.write( "sinx=5/7
\n" ); document.write( "x=45.5847˚
\n" ); document.write( "siny=1/5
\n" ); document.write( "y=191.537
\n" ); document.write( "x+y=237.12˚
\n" ); document.write( "..
\n" ); document.write( "sin(x+y)=sin(237.12)≈-0.8398 (w/calculator)
\n" ); document.write( "exact value as computed=-6√24/35≈-0.8398
\n" ); document.write( "..
\n" ); document.write( "cos(x+y)=cos(237.12)≈-0.5429(w/calculator)
\n" ); document.write( "exact value as computed=-19/35≈-0.5429
\n" ); document.write( "..
\n" ); document.write( "tan(x+y)=tan(237.12)≈1.5469(w/calculator)
\n" ); document.write( "exact value as computed=6√24/19≈1.5470 \n" ); document.write( "