document.write( "Question 1094706: tan(sin^-1(1/7)) \n" ); document.write( "
Algebra.Com's Answer #709254 by Edwin McCravy(20066)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "First we look at the inner part: \r\n" );
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document.write( "That asks for the angle between \"-pi%2F2\" and \"%22%22+%2B+pi%2F2\" whose sine\r\n" );
document.write( "is \"1%2F7\".  \r\n" );
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document.write( "Since we know that \"matrix%281%2C5%2C+sine%2C%22%22=%22%22%2Copposite%2Fhypotenuse%2C%22%22=%22%22%2Cy%2Fr%29\",\r\n" );
document.write( "we draw such an angle by placing a right triangle\r\n" );
document.write( "in the first quadrant whose angle at the origin is such that its\r\n" );
document.write( "opposite side is y=1 and its hypotenuse is r=7, like this:\r\n" );
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document.write( "The angle indicated by the red arc is the angle: .\r\n" );
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document.write( "To find the tangent, we must calculate the adjacent side x,\r\n" );
document.write( "using the Pythagorean theorem:\r\n" );
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document.write( "\"r%5E2\"\"%22%22=%22%22\"\"x%5E2%2By%5E2\"\r\n" );
document.write( "\"7%5E2\"\"%22%22=%22%22\"\"x%5E2%2B1%5E2\"\r\n" );
document.write( "\"49\"\"%22%22=%22%22\"\"x%5E2%2B1\"\r\n" );
document.write( "\"48\"\"%22%22=%22%22\"\"x%5E2\"\r\n" );
document.write( "\"sqrt%2848%29\"\"%22%22=%22%22\"\"x\"\r\n" );
document.write( "\"sqrt%2816%2A3%29\"\"%22%22=%22%22\"\"x\"\r\n" );
document.write( "\"4sqrt%283%29\"\"%22%22=%22%22\"\"x\"\r\n" );
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document.write( "So we now have all three sides of the right triangle:\r\n" );
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document.write( "The problem is \r\n" );
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document.write( "and since we know that \"matrix%281%2C5%2C+tangent%2C%22%22=%22%22%2Copposite%2Fadjacent%2C%22%22=%22%22%2Cy%2Fx%29\"\r\n" );
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document.write( "\"%22%22=%22%22\"\"1%2F%284sqrt%283%29%29\"\"%22%22=%22%22\"\"sqrt%283%29%2F12\".\r\n" );
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document.write( "Edwin
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