document.write( "Question 1101279: Find all solutions in the interval [0, 2π)\r
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Algebra.Com's Answer #715843 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "\"%281%2Btan%5E2%28x%29%29%2B6tan%28x%29=6+\"\r\n" );
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document.write( "\"tan%5E2%28x%29%2B6tan%28x%29%2B1=6+\"\r\n" );
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document.write( "\"tan%5E2%28x%29%2B6tan%28x%29-5=0+\"\r\n" );
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document.write( "\"tan%28x%29%2B6tan%28x%29-5=0+\"\r\n" );
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document.write( "\"tan%28x%29+=+%28-6+%2B-+sqrt%28+6%5E2-4%2A1%2A%28-5%29+%29%29%2F%282%2A1%29+\"\r\n" );
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document.write( "\"tan%28x%29+=+%28-6+%2B-+sqrt%2836%2B20+%29%29%2F2+\"\r\n" );
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document.write( "\"tan%28x%29+=+%28-6+%2B-+sqrt%2856%29%29%2F2+\"\r\n" );
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document.write( "\"tan%28x%29+=+%28-6+%2B-+sqrt%284%2A14%29%29%2F2+\"\r\n" );
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document.write( "\"tan%28x%29+=+%28-6+%2B-+2sqrt%2814%29%29%2F2+\"\r\n" );
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document.write( "\"tan%28x%29+=+%28-6%29%2F2+%2B-+%282sqrt%2814%29%29%2F2+\"\r\n" );
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document.write( "\"tan%28x%29+=+-3+%2B-+sqrt%2814%29+\"\r\n" );
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document.write( "Using the + sign:\r\n" );
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document.write( "\"tan%28x%29+=+-3+%2B+sqrt%2814%29+\"\r\n" );
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document.write( "Approximation:\r\n" );
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document.write( "\"tan%28x%29+=+0.7416573868\"\r\n" );
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document.write( "The tangent is positive in quadrants I and III.\r\n" );
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document.write( "We find the reference angle by using the absolute value,\r\n" );
document.write( "that is, we find the inverse tangent of +0.7416573868. \r\n" );
document.write( "Make sure your calculator is in radian mode:\r\n" );
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document.write( "To get the answer in quadrant I, use the reference\r\n" );
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document.write( "\"x=0.6381404208\"   <-- that's one solution\r\n" );
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document.write( "To get the answer in quadrant III, add p to the\r\n" );
document.write( "reference angle.\r\n" );
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document.write( "\"x=0.6381404208%2B3.141592654\"\r\n" );
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document.write( "\"x=3.779733074\"   <-- that's a second solution\r\n" );
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document.write( "Using the - sign:\r\n" );
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document.write( "\"tan%28x%29+=+-3+-+sqrt%2814%29+\"\r\n" );
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document.write( "Approximation:\r\n" );
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document.write( "\"tan%28x%29+=+-6.741657387\"\r\n" );
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document.write( "The tangent is negative in quadrants II and IV.\r\n" );
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document.write( "We find the reference angle by using the absolute value,\r\n" );
document.write( "that is, we find the inverse tangent of +6.741657387. \r\n" );
document.write( "Make sure your calculator is still in radian mode:\r\n" );
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document.write( "To get the answer in quadrant II, subtract the reference\r\n" );
document.write( "angle from p\r\n" );
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document.write( "\"3.141592654-1.423538584\"\r\n" );
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document.write( "\"x=1.71805407\"   <-- that's a third solution\r\n" );
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document.write( "To get the answer in quadrant IV, subtract the reference\r\n" );
document.write( "angle from 2p.\r\n" );
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document.write( "\"x=2%283.141592654%29-1.71805407\"\r\n" );
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document.write( "\"x=4.565131237\"   <-- that's a fourth solution\r\n" );
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document.write( "Edwin
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