document.write( "Question 1209453: find all solutions:
\n" ); document.write( "3sin^2x+2sinx-1=0; in the interval [0,2pi) \n" ); document.write( "

Algebra.Com's Answer #848861 by ikleyn(52782) $\"\"$ $\"About$

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\n" ); document.write( "find all solutions:
\n" ); document.write( "3sin^2x+2sinx-1=0; in the interval [0,2pi)
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document.write( "Introduce new variable  u = sin(x).\r\n" );
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document.write( "Then your equation takes the form\r\n" );
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document.write( "    3u^2 + 2u - 1 = 0.\r\n" );
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document.write( "Factorize\r\n" );
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document.write( "    (3u-1)*(u+1) = 0.\r\n" );
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document.write( "Its roots are  u = 1/3  and  u= -1.\r\n" );
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document.write( "So, we consider now two cases\r\n" );
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document.write( "    (a)  sin(x) = 1/3,  which gives two solutions  x =   and  x =  - .\r\n" );
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document.write( "    (b)  sin(x) = -1,   which gives the solution   x =   = .\r\n" );
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document.write( "At this point, the problem is solved completely.\r\n" );
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document.write( "ANSWER.  The solutions to the given equation in the given interval are  ,   -   and  .\r\n" );
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