document.write( "Question 196162: How can you find the asymptotes of cotangent, cosecant, and secant problems?
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\n" ); document.write( "\n" ); document.write( "1. What are the asymptotes of \"g%28x%29=+cot%280.5x%29\"
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\n" ); document.write( "3. What are the asymptotes of \"g%28x%29+=+%281%2F2%29csc%28x%29\" \n" ); document.write( "
Algebra.Com's Answer #147092 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "There are infinitely many asymptotes for each of\r\n" );
document.write( "these.\r\n" );
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document.write( "Rules:\r\n" );
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document.write( "To find asymptotes for \r\n" );
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document.write( "        Tangent and secant graphs\r\n" );
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document.write( "Set the argument (what the tangent or secant is of)\r\n" );
document.write( "equal to \"%282n%2B1%29%2Api%2F2\" and solve for x.\r\n" );
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document.write( "Then let n = any integer, positive, negative, or zero.\r\n" );
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document.write( "        Cotangent and cosecant graphs\r\n" );
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document.write( "Set the argument (what the cotangent or cosecant is of)\r\n" );
document.write( "equal to \"n%2Api\" and solve for x.\r\n" );
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document.write( "Then let n = any integer, positive, negative, or zero.\r\n" );
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document.write( "[Note: the asymptotes are not affected by a coefficient\r\n" );
document.write( "in front of the trig function]\r\n" );
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\n" ); document.write( "1. What are the asymptotes of \"g%28x%29=+cot%280.5x%29\"
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document.write( "This is a cotangent graph, so set\r\n" );
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document.write( "\"0.5x+=+n%2Api\"\r\n" );
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document.write( "Remove the decimal by multiplying both sides by 10\r\n" );
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document.write( "\"5x+=+10n%2Api\"\r\n" );
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document.write( "\"x+=+%2810n%2Api%29%2F5\"\r\n" );
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document.write( "\"x+=+2n%2Api\"  \r\n" );
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document.write( "Let n = -3, -2, -1, 0, 1, 2, 3\r\n" );
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document.write( "\"x+=+2%28-3%29%2Api\",\"x+=+2%28-2%29%2Api\", \"x+=+2%28-1%29%2Api\",\"x+=+2%280%29%2Api\", \"x+=+2%281%29%2Api\", \"x+=+2%282%29%2Api\", \"x+=+2%283%29%2Api\", etc., etc.,\r\n" );
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document.write( "This becomes:\r\n" );
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document.write( "\"x+=+-6pi\",\"x+=+-4pi\", \"x+=+-2pi\",\"x+=+0\", \"x+=+2pi\", \"x+=+4pi\", \"x+=+6pi\", etc., etc.,\r\n" );
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document.write( "These are all asymptotes.\r\n" );
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\n" ); document.write( "2. What are the asymptotes of \"g%28x%29+=+sec%282x%29\"
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document.write( "This is a secant graph, so set\r\n" );
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document.write( "\"2x+=+%282n%2B1%29%2Api%2F2\"\r\n" );
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document.write( "\"x+=+%28%282n%2B1%29%2Api%2F2%29%2F2\"\r\n" );
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document.write( "\"x+=+%282n%2B1%29%2Api%2F2%7D%2A%281%2F2%29\"\r\n" );
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document.write( "\"x+=+%282n%2B1%29%2Api%2F4\"\r\n" );
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document.write( "  Let n = -3, -2, -1, 0, 1, 2, 3\r\n" );
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document.write( "\"x+=+%282%28-3%29%2B1%29%2Api%2F4\",\"x+=+%282%28-2%29%2B1%29%2Api%2F4\",\"x+=+%282%28-1%29%2B1%29%2Api%2F4\",\"x+=+%282%280%29%2B1%29%2Api%2F4\",\"x+=+%282%281%29%2B1%29%2Api%2F4\",\"x+=+%282%282%29%2B1%29%2Api%2F4\",\"x+=+%282%283%29%2B1%29%2Api%2F4\"\r\n" );
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document.write( "This becomes:\r\n" );
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document.write( "\"x+=+-5pi%2F4\",\"x+=+-3pi%2F4\", \"x+=+-pi%2F4\",\"x+=+pi%2F4\", \"x+=+3pi%2F4\", \"x+=+5pi%2F4\", \"x+=+7pi%2F4\", etc., etc.,\r\n" );
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document.write( "These are all asymptotes.\r\n" );
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\n" ); document.write( "3. What are the asymptotes of \"g%28x%29+=+%281%2F2%29csc%28x%29\"
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document.write( "Note: The \"1%2F2\" in front does not affect the asymptotes,\r\n" );
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document.write( "This is a cosecant graph, so set\r\n" );
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document.write( "\"x+=+n%2Api\"\r\n" );
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document.write( "Let n = -3, -2, -1, 0, 1, 2, 3\r\n" );
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document.write( "\"x+=+-3pi\",\"x+=+-2pi\", \"x+=+-pi\",\"x+=+0\", \"x+=+pi\", \"x+=+2pi\", x = 3pi, etc., etc.,\r\n" );
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document.write( "These are all asymptotes.\r\n" );
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document.write( "Edwin
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