document.write( "Question 809218: Find the first three x-intercepts of the graph of the given function on the positive x-axis.\r
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Algebra.Com's Answer #487502 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "The other tutor gave decimals and also missed solutions.  I think your teacher wanted\r\n" );
document.write( "exact values, which as you will see are , ,   \r\n" );
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document.write( "f(x) = 9 - 18cos(x+)\r\n" );
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document.write( "9 - 18cos(x+) = 0\r\n" );
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document.write( "   -18cos(x+) = -9\r\n" );
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document.write( "      cos(x+) = \r\n" );
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document.write( "The angles whose cosine is  have reference angle 60° in QI and QIV\r\n" );
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document.write( "x+  =  and x+ = \r\n" );
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document.write( "where n is an integer.\r\n" );
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document.write( "Solve the first equation:\r\n" );
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document.write( "x+  = \r\n" );
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document.write( "   x = \r\n" );
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document.write( "We require that solutions be on the positive x-axis\r\n" );
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document.write( "2n*pi > 0, so n = 1,2,...\r\n" );
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document.write( "Solutions for that are , , , etc.\r\n" );
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document.write( "Those are approximately 6.3, 12.6, 18.8, etc.\r\n" );
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document.write( "(I'm using decimals only to tell which are the smallest three exact\r\n" );
document.write( "solutions, not for final answers)\r\n" );
document.write( "   \r\n" );
document.write( "Solve the second equation:\r\n" );
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document.write( "x+ = \r\n" );
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document.write( "  x = \r\n" );
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document.write( "  x = \r\n" );
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document.write( "  x = \r\n" );
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document.write( "  x = \r\n" );
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document.write( "We require\r\n" );
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document.write( " > 0\r\n" );
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document.write( " > 0\r\n" );
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document.write( "4 + 6n > 0\r\n" );
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document.write( "    6n > -4\r\n" );
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document.write( "     n > \r\n" );
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document.write( "     n > \r\n" );
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document.write( "So n = 0, 1, 2, ...\r\n" );
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document.write( "Solutions on the positive x-axis for are \r\n" );
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document.write( ", , , etc.\r\n" );
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document.write( "or\r\n" );
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document.write( ", ,  , etc.\r\n" );
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document.write( "Those are approximately 4.2, 10.5, 16.8, etc.\r\n" );
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document.write( "(I'm using decimals only to tell which are the smallest three exact\r\n" );
document.write( "solutions)\r\n" );
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document.write( "So the smallest is the one that is approximately 4.2, which is .\r\n" );
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document.write( "The next one after that is the one that is approximately 6.3 or .\r\n" );
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document.write( "The next one after that is the one that is approximately 10.5 or \r\n" );
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document.write( "Answers: , , \r\n" );
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document.write( "Edwin

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