document.write( "Question 149437: Solve for roots\r
\n" ); document.write( "\n" ); document.write( "3sin^2x-8sinx-3=0 \n" ); document.write( "

Algebra.Com's Answer #109727 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"3%2Asin%5E2%28x%29-8%2Asin%28x%29-3=0\"$
\n" ); document.write( "Let's substitute $\"u=sin%28x%29\"$
\n" ); document.write( " $\"3u%5E2-8u-3=0\"$ Quadratic equation in u.
\n" ); document.write( " $\"%283u%2B1%29%28u-3%29=0\"$ Factor the quadratic equation.
\n" ); document.write( "First factor:
\n" ); document.write( " $\"3u%2B1=0\"$
\n" ); document.write( " $\"3sin%28x%29%2B1=0\"$
\n" ); document.write( " $\"3sin%28x%29=-1\"$
\n" ); document.write( " $\"sin%28x%29=-1%2F3\"$
\n" ); document.write( "2 solutions for this equation.
\n" ); document.write( "x=340.53 degrees and x=199.47 degrees
\n" ); document.write( "Second factor:
\n" ); document.write( " $\"u-3=0\"$
\n" ); document.write( " $\"sin%28x%29-3=0\"$
\n" ); document.write( " $\"sin%28x%29=3\"$
\n" ); document.write( "sin(x) is never greater than 1, so there are no additional solutions.
\n" ); document.write( "Below is the graph of the function.
\n" ); document.write( " $\"+graph%28+300%2C+200%2C+0%2C+7%2C+-10%2C10%2C+3%2A%28sin%28x%29%5E2%29-8%2Asin%28x%29-3%29+\"$
\n" ); document.write( "Note : x axis is measured in radians.
\n" ); document.write( "360 degrees = 6.28 radians
\n" ); document.write( "340.53 degrees = 5.94 radians
\n" ); document.write( "199.47 degrees = 3.48 radians \n" ); document.write( "

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