document.write( "Question 819578: Find the exact value of the expression\r
\n" ); document.write( "\n" ); document.write( "sin((tan^-1 3/4) +(cos^-1 5/13)) \n" ); document.write( "
Algebra.Com's Answer #493172 by lwsshak3(11628)\"\" \"About 
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Find the exact value of the expression
\n" ); document.write( "sin((tan^-1 3/4) +(cos^-1 5/13))
\n" ); document.write( "***
\n" ); document.write( "let x=angle whose tan=3/4
\n" ); document.write( "let y=angle whose cos=5/13
\n" ); document.write( "Identity: sin(x+y)=sinxcosy+cosxsiny
\n" ); document.write( "..
\n" ); document.write( "tanx=3/4(this is from a (3-4-5) right triangle)
\n" ); document.write( "sinx=3/5
\n" ); document.write( "cosx=4/5
\n" ); document.write( "..
\n" ); document.write( "cosy=5/13(this is from a (5-12-13) right triangle)
\n" ); document.write( "siny=12/13
\n" ); document.write( "..
\n" ); document.write( "sin((tan^-1 3/4) +(cos^-1 5/13))=sin(x+y)
\n" ); document.write( "sin(x+y)=3/5*5/13+4/5*12/13=15/65+48/65=63/65
\n" ); document.write( "..
\n" ); document.write( "calculator check:
\n" ); document.write( "tanx=3/4
\n" ); document.write( "x≈36.87˚
\n" ); document.write( "cosy=5/13
\n" ); document.write( "x≈67.38˚
\n" ); document.write( "(x+y)≈104.25
\n" ); document.write( "sin(x+y)≈sin(104.25)≈0.9692..
\n" ); document.write( "Exact value as calculated=63/65≈0.9692..
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