document.write( "Question 923447: Suppose sin x = 1/7
\n" ); document.write( "cos x > 0, sin y = −2/5
\n" ); document.write( "and cos y < 0. Then \r
\n" ); document.write( "\n" ); document.write( "cos x =
\n" ); document.write( "cos y = \r
\n" ); document.write( "\n" ); document.write( "Find each of the following quantities:\r
\n" ); document.write( "\n" ); document.write( "sin(x + y) = \r
\n" ); document.write( "\n" ); document.write( "cos(x + y) = \r
\n" ); document.write( "\n" ); document.write( "tan(x + y) \n" ); document.write( "
Algebra.Com's Answer #560235 by lwsshak3(11628)\"\" \"About 
You can put this solution on YOUR website!
Suppose sin x = 1/7
\n" ); document.write( "cos x > 0, sin y = −2/5
\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( "reference angle x is in quadrant I where sin>0, cos>0
\n" ); document.write( "sinx=1/7
\n" ); document.write( "cosx=√(1-sin^2x)=√(1-1/49)=√(48/49)=√48/7)
\n" ); document.write( "..
\n" ); document.write( "reference angle y is in quadrant III where sin<0, cos<0
\n" ); document.write( "siny=-2/5
\n" ); document.write( "cosy=-√(1-sin^2y)=-√(1-4/25)=-√(21/25)=-√21/5
\n" ); document.write( "..
\n" ); document.write( "sin(x+y)=sinxcosy+cosxsiny=1/7*-√21/5+√48/7*-2/5=-√21/35-2√48/35=-(√21+2√48)/35
\n" ); document.write( "cos(x+y)=cosxcosy-sinxsiny=√48/7*-√21/5-1/7*-2/5=-√1008/35+2/35=(-√1008+2)/35
\n" ); document.write( "tan(x+2)=sin(x+2)/cos(x+2)=-(√21+2√48)/(-√1008+2)\r
\n" ); document.write( "\n" ); document.write( "check:
\n" ); document.write( "sinx=1/7
\n" ); document.write( "x≈8.21˚
\n" ); document.write( "siny=-2/5
\n" ); document.write( "y≈203.58˚
\n" ); document.write( "x+y≈203.58+8.21≈211.79
\n" ); document.write( "..
\n" ); document.write( "sin(x+y)≈sin(211.79)≈-0.5268 (w/calculator)
\n" ); document.write( "exact value as computed=-(√21+2√48)/35≈-0.5268
\n" ); document.write( "..
\n" ); document.write( "cos(x+y)≈cos(211.79)≈-0.8500 (w/calculator)
\n" ); document.write( "exact value as computed=(-√1008+2)/35≈-0.8500
\n" ); document.write( "..
\n" ); document.write( "tan(x+y)=tan(211.79)≈0.6198 (w/calculator)
\n" ); document.write( "exact value as computed=-(√21+2√48)/(-√1008+2)≈.5268/.8500≈0.6198
\n" ); document.write( " \n" ); document.write( "
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