document.write( "Question 901911: Solve the trigonometric inequality. Write the solution in interval notation.\r
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Algebra.Com's Answer #547025 by Edwin McCravy(20065)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "2cos²(3x) + 5cos(3x) - 3 < 0\r\n" );
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document.write( "The left factors just as 2u²+5u-3 = (u+3)(2u-1)\r\n" );
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document.write( "[cos(3x)+3][2cos(3x)-1] < 0\r\n" );
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document.write( "We find the critical values by finding the zeros of the left side\r\n" );
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document.write( "The first factor has no zeros since no cosine can be -3\r\n" );
document.write( "The second factor has zeros when cos(3x) = \"1%2F2\"\r\n" );
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document.write( "This is when \"3x=pi%2F3+%2B2n%2Api\"   and when \"3x=5pi%2F3%2B2n%2Api\"\r\n" );
document.write( "             \"x=pi%2F9+%2B2n%2Api%2F3\"          \"x=5pi%2F9%2B2n%2Api%2F3\" \r\n" );
document.write( "             \"x=pi%2F9+%2B6n%2Api%2F9\"          \"x=5pi%2F9%2B6n%2Api%2F9\"\r\n" );
document.write( "             \"x=expr%28pi%2F9%29%281%2B6n%29\"            \"x=expr%28%285pi%29%2F9%29%285%2B6n%29\"\r\n" );
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document.write( "\"graph%28400%2C400%2C-2pi%2C2pi%2C-7%2C5%2C2cos%283x%29%5E2%2B5cos%283x%29-3%29\"\r\n" );
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document.write( "From the graph of y = 2cos²(3x) + 5cos(3x) - 3 we see that the graph is negative\r\n" );
document.write( "(below the x-axis) in all open intervals\r\n" );
document.write( ", when n is any integer.       \r\n" );
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document.write( "Edwin
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