document.write( "Question 33862: 
cosq = 5/12 and tanq is negative, find the exact value for cscq.

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Algebra.Com's Answer #20275 by AnlytcPhil(1806)\"\" \"About 
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cosq = 5/12 and tanq is negative, find the exact value for cscq.\r\n" );
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document.write( "5/12 is a positive number and the cosine is positive in I and IV,\r\n" );
document.write( "the tangent is negative in II and IV.  So, q can only be in IV.\r\n" );
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document.write( "Draw a picture          |\r\n" );
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document.write( "                        | x\r\n" );
document.write( "                 -------|---------\r\n" );
document.write( "                        |\   |\r\n" );
document.write( "                        | \  |y\r\n" );
document.write( "                        | r\ |\r\n" );
document.write( "                        |   \|\r\n" );
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document.write( "Since cosq = 5/12 = x/r, put 5 for the x and 12 for the r\r\n" );
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document.write( "Draw a picture          |\r\n" );
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document.write( "                        | 5\r\n" );
document.write( "                 -------|---------\r\n" );
document.write( "                        |\   |\r\n" );
document.write( "                        | \  |y\r\n" );
document.write( "                        |12\ |\r\n" );
document.write( "                        |   \|\r\n" );
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document.write( "Use the Pythagorean theorem \r\n" );
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document.write( "                     x² + y² = r²\r\n" );
document.write( "                     5² + y² = 12²\r\n" );
document.write( "                     25 + y² = 144\r\n" );
document.write( "                          y² = 119\r\n" );
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document.write( "                           y = ±Ö119\r\n" );
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document.write( "Since y goes down, we select the negative sign.\r\n" );
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document.write( "                           y = -Ö119\r\n" );
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document.write( "You are asked to find the cscq.\r\n" );
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document.write( "cscq = r/y = 12/(-Ö119) = -12/Ö119\r\n" );
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document.write( "Edwin\r\n" );
document.write( "AnlytcPhil@aol.com
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