document.write( "Question 775020: solve 2sinx-4cosx=3 \n" ); document.write( "

Algebra.Com's Answer #472790 by lwsshak3(11628) $\"\"$ $\"About$

You can put this solution on YOUR website!
solve 2sinx-4cosx=3
\n" ); document.write( " $\"2sin%28x%29-4cos%28x%29=3\"$
\n" ); document.write( " $\"2sin%28x%29-4sqrt%281-sin%5E2%28x%29%29=3\"$
\n" ); document.write( " $\"2sin%28x%29-3=4sqrt%281-sin%5E2%28x%29%29\"$
\n" ); document.write( "square both sides
\n" ); document.write( " $\"4sin%5E2%28x%29-12sin%28x%29%2B9=16%281-sin%5E2%28x%29%29\"$
\n" ); document.write( " $\"4sin%5E2%28x%29-12sin%28x%29%2B9=16-16sin%5E2%28x%29%29\"$
\n" ); document.write( " $\"20sin%5E2%28x%29-12sin%28x%29-7=0\"$
\n" ); document.write( "solve for sin(x) using quadratic formula:
\n" ); document.write( " $\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"$
\n" ); document.write( "a=20, b=-12, c=-7
\n" ); document.write( "sin(x)≈-0.3633
\n" ); document.write( "x≈201.30º and 338.30º
\n" ); document.write( "or
\n" ); document.write( "sin(x)≈0.9633
\n" ); document.write( "x≈74.43º and 105.57º \n" ); document.write( "

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