document.write( "Question 925334: Evaluate:\r
\n" ); document.write( "\n" ); document.write( "sin(x + y) if sin x =3/5, sec x > 0, cos y = − 2√(5)/5, and tan y < 0\r
\n" ); document.write( "\n" ); document.write( "sin(x + y) = \n" ); document.write( "

Algebra.Com's Answer #561504 by lwsshak3(11628) $\"\"$ $\"About$

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Evaluate:
\n" ); document.write( "sin(x + y) if sin x =3/5, sec x > 0, cos y = − 2√(5)/5, and tan y < 0
\n" ); document.write( "sin(x + y) =
\n" ); document.write( "***
\n" ); document.write( "sinx=3/5
\n" ); document.write( "secx>0
\n" ); document.write( "reference angle x is in quadrant I where sin>0, cos>0
\n" ); document.write( "cosx=4/5 (working with (3-4-5) reference right triangle in quadrant I)
\n" ); document.write( "...
\n" ); document.write( "cosy=-2√5/5
\n" ); document.write( "tany<0
\n" ); document.write( "reference angle y is in quadrant II where sin>0, cos<0
\n" ); document.write( "siny=√(1-cos^2(y))=√(1-20/25)=√(5/25)=√5/5
\n" ); document.write( "..
\n" ); document.write( "sin(x+y)=sinxcosy+cosxsiny=3/5*-2√5/5+4/5*√5/5=-6√5/25+4√5/25=-2√5/25
\n" ); document.write( "..
\n" ); document.write( "Check:
\n" ); document.write( "sinx=3/5
\n" ); document.write( "x≈36.87˚
\n" ); document.write( "cosy=-2√5/5
\n" ); document.write( "y≈153.43˚
\n" ); document.write( "x+y≈190.30˚
\n" ); document.write( "sin(x+y)≈sin(190.30)≈-0.1788
\n" ); document.write( "exact value as computed=-2√5/25≈-0.1788 \n" ); document.write( "

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