document.write( "Question 1101265: Find all solutions in degress in the interval [0,360]\r
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Algebra.Com's Answer #715837 by ikleyn(52908) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "Instruction from Alan is correct, but I think that for the person who posted it, it is not enough.\r\n" );
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document.write( "So I put the entire solution here.\r\n" );
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document.write( "Introduce new variable u = cos(x). Then your equation takes the form\r\n" );
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document.write( "6u^2 + 7u + 2 = 0.\r\n" );
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document.write( "It is QUADRATIC EQUATION for the unknown \"u\". To solve it, apply the quadratic formula\r\n" );
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document.write( " =  = .\r\n" );
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document.write( "You have two solutions for u:\r\n" );
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document.write( "1)   =  =  = .\r\n" );
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document.write( "    It leads us to equation cos(x) =  which has TWO solutions x = 120 degs and/or x = 240 degs in the given interval.\r\n" );
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document.write( "2)   =  =  = .\r\n" );
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document.write( "     It leads to equation cos(x) =  which has TWO solutions x = arccos(-2/3) degs and/or x = arccos(-2/3) degs + 180 degs  in the given interval.\r\n" );
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document.write( "Answer.  The given equation has 4 (four) solutions:\r\n" );
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document.write( "         x= 120 degs;  x= 240 degs;  x= arccos(-2/3) degs  and  x = arccos(-2/3) degs + 180 degs.\r\n" );
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