Algebra.Com's Answer #360960 by AnlytcPhil(1806)![\"\"](\"/images/stars/stars-12.gif\")  
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If cotq = -3/4 and sinq < 0, then the value of cosq is:
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document.write( "The cotangent, being  is negative, and the cotangent is \r\n" );
document.write( "negative in quadrants II and IV\r\n" );
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document.write( "The sine, being < 0, is negative, and the sine is \r\n" );
document.write( "negative in quadrants III and IV.\r\n" );
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document.write( "Therefore q is in quadrant IV\r\n" );
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document.write( "The cotangent is  =  \r\n" );
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document.write( "So we draw a triangle in quadrant IV with its hypotenuse as\r\n" );
document.write( "the terminal side of q, its shorter leg x=+3 and its longer leg \r\n" );
document.write( "y=-4. The shorter leg will be taken positive since it goes right,\r\n" );
document.write( "and the longer leg will be taken negative because it goes down. \r\n" );
document.write( "The angle q is indicated by the red arc.\r\n" );
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document.write( "Now we calculate r, the hypotenuse, by the Pythagorean theorem:\r\n" );
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document.write( "r² = x² + y²\r\n" );
document.write( "r² = (3)² + (-4)²\r\n" );
document.write( "r² = 9 + 16\r\n" );
document.write( "r² = 25\r\n" );
document.write( " r = 5\r\n" );
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document.write( "Now since we want cos(q), we know that cos(q) =  =  .\r\n" );
document.write( "It is positive as we would expect an angle's cosine to be in quadrant IV.\r\n" );
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document.write( "Edwin
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