document.write( "Question 1102259: sin(2x) = -sqrt(2)/2\r
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Algebra.Com's Answer #717020 by ikleyn(52834) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "The solution by @Lightning_Fast is partly WRONG and partly INCOMPLETE, so NEITHER PART OF HIS SOLUTION IS USEFUL.\r
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\n" ); document.write( "\n" ); document.write( "Below please find the CORRECT solution.\r
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document.write( "sin(2x) =   ======================>\r\n" );
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document.write( "This equation has two solutions for 2x:\r\n" );
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document.write( "1)  2x =    or   2)  2x = .\r\n" );
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document.write( "Case 1.  2x =   has TWO solutions for the angle x:  \r\n" );
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document.write( "                                                   a)  x =   and\r\n" );
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document.write( "                                                   b)  x =  = .\r\n" );
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document.write( "Case 2.  2x =   has TWO solutions for the angle x:  \r\n" );
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document.write( "                                                   a)  x =   and\r\n" );
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document.write( "                                                   b)  x =  = .\r\n" );
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document.write( "Answer.  The given equation has four solutions:  ,  ,    and  .\r\n" );
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\n" ); document.write( "\n" ); document.write( "The plot below CONFIRMS existing of four solutions in the interval [0, $\"2pi\"$ ):\r
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\n" ); document.write( "\n" ); document.write( "Plot y = sin(2x) (red) and y = $\"-sqrt%282%29%2F2\"$ (green)\r
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