document.write( "Question 148692: what is the sine of an angle whose tangent is 2? first find an answer without a calculator, then check it with one.\r
\n" ); document.write( "\n" ); document.write( "thank you! \n" ); document.write( "

Algebra.Com's Answer #109049 by Fombitz(32388) $\"\"$ $\"About$

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From trigonometry, you know the following identities, where
\n" ); document.write( "Opp = Length of triangle leg opposite to angle x.
\n" ); document.write( "Adj = Length of triangle leg adjacent to angle x.
\n" ); document.write( "Hyp = Hypotenuse of triangle with sides Opp and Adj.
\n" ); document.write( "Tan(x)=Opp/Adj
\n" ); document.write( "Sin(x)=Opp/Hyp
\n" ); document.write( "Cos(x)=Adj/Hyp
\n" ); document.write( " $\"Sin%5E2%28x%29%2BCos%5E2%28x%29=1\"$
\n" ); document.write( "Since Tan(x)=2, then
\n" ); document.write( "Opp/Adj = 2
\n" ); document.write( "Opp = 2 Adj
\n" ); document.write( "Opp/Hyp = 2 Adj/Hyp
\n" ); document.write( "Sin(x) = 2 Cos(x)
\n" ); document.write( " $\"%282+Cos%28x%29%29%5E2%2BCos%5E2%28x%29=1\"$
\n" ); document.write( " $\"4%2ACos%5E2%28x%29%2BCos%5E2%28x%29=1\"$
\n" ); document.write( " $\"5%2ACos%5E2%28x%29=1\"$
\n" ); document.write( " $\"Cos%5E2%28x%29=1%2F5\"$
\n" ); document.write( " $\"Cos%28x%29=1%2Fsqrt%285%29\"$
\n" ); document.write( " $\"Cos%28x%29=.4472\"$
\n" ); document.write( "Checking the sine tables,
\n" ); document.write( "0.4478 for 63.4
\n" ); document.write( "0.4462 for 63.5
\n" ); document.write( "We can set up a proportion to get an approximate answer,
\n" ); document.write( " $\"%2863.4-x%29%2F%2863.4-63.5%29=%280.4478-0.4472%29%2F%280.4478-0.4462%29\"$
\n" ); document.write( " $\"%2863.4-x%29%2F%28-0.1%29=%280.0006%29%2F%280.0016%29\"$
\n" ); document.write( " $\"63.4-x=-.0375\"$
\n" ); document.write( " $\"x=63.44\"$
\n" ); document.write( "From the calculator,
\n" ); document.write( "x=63.43 \n" ); document.write( "

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