document.write( "Question 872079: value of \"sin%28cot%5E-1+%28x%29%29\" \n" ); document.write( "
Algebra.Com's Answer #525914 by Edwin McCravy(20081)\"\" \"About 
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document.write( "sin(cot-1(x))\r\n" );
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document.write( "The way to interpret that problem is:\r\n" );
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document.write( "\"Find the sine of the angle whose cotangent is x.\"\r\n" );
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document.write( "Let that angle be q.\r\n" );
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document.write( "We know that \"cotangent\"\"%22%22=%22%22\"\"%28adjacent%29%2F%28opposite%29\"\r\n" );
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document.write( "We also know that x can be written as \"x%2F1\"\r\n" );
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document.write( "So we draw a right triangle containing the angle q\r\n" );
document.write( "with the side that is adjacent to q having length x\r\n" );
document.write( "and the side that is opposite to angle q be 1.\r\n" );
document.write( "Like this:\r\n" );
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document.write( "We have drawn a right triangle containing an angle whose\r\n" );
document.write( "cotangent is \"x%2F1\" which is x.\r\n" );
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document.write( "Now we calculate the hypotenuse by the Pythagorean theorem,\r\n" );
document.write( "because we'll need that to find the sine.\r\n" );
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document.write( "hypotenuse2 = adjacent2+opposite2\r\n" );
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document.write( "hypotenuse2 = x2+12\r\n" );
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document.write( "hypotenuse = √x²+1\r\n" );
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document.write( "Now, we remember that the way to interpret the problem\r\n" );
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document.write( "sin(cot-1(x))\r\n" );
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document.write( "is:\r\n" );
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document.write( "\"Find the sine of the angle whose cotangent is x.\"\r\n" );
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document.write( "And we let that angle be q.\r\n" );
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document.write( "So since \"sine\"\"%22%22=%22%22\"\"%28opposite%29%2F%28hypotenuse%29\" \r\n" );
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document.write( "then,\r\n" );
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document.write( "sin(cot-1(x)) = sin(q) = \"1%2Fsqrt%28x%5E2%2B1%29\".\r\n" );
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document.write( "Edwin
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