document.write( "Question 744764: Evaluate the given expression without using a calculator. (Assume any variables represent positive numbers)\r
\n" ); document.write( "\n" ); document.write( "Sin( arccos 3/5 + arctan 1/2) \n" ); document.write( "

Algebra.Com's Answer #453537 by lwsshak3(11628) $\"\"$ $\"About$

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Evaluate the given expression without using a calculator. (Assume any variables represent positive numbers)
\n" ); document.write( "Sin( arccos 3/5 + arctan 1/2)
\n" ); document.write( "***
\n" ); document.write( "let x=arccos 3/5
\n" ); document.write( "let y=arctan 1/2
\n" ); document.write( "..
\n" ); document.write( " $\"cos%28x%29=3%2F5\"$
\n" ); document.write( " $\"sin%28x%29=sqrt%281-cos%5E2%28x%29%29=sqrt%281-9%2F25%29=sqrt%2816%2F25%29=4%2F5\"$
\n" ); document.write( "..
\n" ); document.write( " $\"tan%28y%29=1%2F2=sin%28y%29%2Fcos%28y%29\"$
\n" ); document.write( " $\"sin%28y%29=1%2Fsqrt%285%29\"$
\n" ); document.write( " $\"cos%28y%29=2%2Fsqrt%285%29\"$
\n" ); document.write( "..
\n" ); document.write( "Sin( arccos 3/5 + arctan 1/2)=sin(x+y)
\n" ); document.write( "=sin(x) cos(y)+cos(x) sin(y)
\n" ); document.write( "=4/5*2/√5+3/5*1/√5
\n" ); document.write( "=8/5√5+3/5√5=11/(5√5)
\n" ); document.write( "=(11√5)/25
\n" ); document.write( "..
\n" ); document.write( "Check: (with calculator)
\n" ); document.write( "cos(x)=3/5
\n" ); document.write( "x≈53.13º
\n" ); document.write( "tan(y)=1/2
\n" ); document.write( "y≈26.57º
\n" ); document.write( "x+y≈79.7º
\n" ); document.write( "sin(x+y)=sin79.7º≈0.9839
\n" ); document.write( "exact answer=(11√5)/25≈0.9839 \n" ); document.write( "

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