document.write( "Question 974077: How many times does the graph of f(x) = cos(x) intersect the graph of g(x) = cos(2x) in the interval [0, 2 pi]? \n" ); document.write( "
Algebra.Com's Answer #596094 by Edwin McCravy(20055)\"\" \"About 
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How many times does the graph of f(x) = cos(x) intersect the graph of g(x) = cos(2x) in the interval [0, 2 pi]?
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document.write( "To find where they intersect we set f(x) = g(x)\r\n" );
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document.write( "cos(x) = cos(2x)\r\n" );
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document.write( "cos(x) = 2cosē(x) - 1\r\n" );
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document.write( "     0 = 2cosē(x) - cos(x) - 1\r\n" );
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document.write( "We factor the right side\r\n" );
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document.write( "     0 = [2cos(x) + 1][cos(x) - 1]\r\n" );
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document.write( "Use the zero-factor property:\r\n" );
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document.write( "2cos(x) + 1 = 0;         cos(x) - 1 = 0 \r\n" );
document.write( "    2cos(x) = 1;             cos(x) = 1\r\n" );
document.write( "     cos(x) = \"1%2F2\";                x = 0, 2p\r\n" );
document.write( "          x = \"pi%2F3\",\"5pi%2F3\"\r\n" );
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document.write( "Answer: four times since we include both 0 and 2p,\r\n" );
document.write( "and the interval is given with brackets on both sides [0,2p]\r\n" );
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document.write( "\"graph%28400%2C3000%2F17%2C-.5%2C6.3%2C-1.5%2C1.5%2Ccos%28x%29%2Ccos%282x%29%29\"\r\n" );
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document.write( "Edwin
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