document.write( "Question 1105695: solve 2sin²x -5sinx-3=0 \n" ); document.write( "

Algebra.Com's Answer #720576 by math_helper(2461) $\"\"$ $\"About$

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solve 2sin²x -5sinx-3=0
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\n" ); document.write( "\n" ); document.write( "I will solve $\"+2sin%5E2%28x%29+-+5sin%28x%29+-+3+=+0\"$ for $\"+0%3C=+x+%3C=+2pi+\"$ \r
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\n" ); document.write( "\n" ); document.write( "Let u = sin(x)\r
\n" ); document.write( "\n" ); document.write( "Then $\"+2u%5E2+-+5u+-+3+=+0+\"$
\n" ); document.write( " $\"+%282u+%2B+1%29%28u+-+3%29+=+0+\"$
\n" ); document.write( " $\"+u=-1%2F2+\"$ and $\"+u=3+\"$ \r
\n" ); document.write( "\n" ); document.write( "Substitute back in for u:
\n" ); document.write( " $\"+sin%28x%29+=+-1%2F2+\"$ and $\"+sin%28x%29+=+3+\"$
\n" ); document.write( " $\"+sin%28x%29+=+3+\"$ has no solution, discard it.\r
\n" ); document.write( "\n" ); document.write( " $\"sin%28x%29+=+-1%2F2+\"$ —> $\"++x+=+-pi%2F6+\"$ or $\"+x+=+highlight%28%2811pi%29%2F6+%29+\"$ (Q4 angle)
\n" ); document.write( " There is also a Q3 angle: $\"+x+=+pi+%2B+abs%28%28-pi%2F6%29%29+=+highlight%28%287pi%29%2F6%29+\"$ (Q3 angle)\r
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