document.write( "Question 855223: Find the exact value of the expression, if it is defined
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Algebra.Com's Answer #515176 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "The other tutor mistakenly took your word \"exact\" \r\n" );
document.write( "for \"approximate\". \r\n" );
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document.write( "The convention for inverse tangent is:\r\n" );
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document.write( "0 < tan-1(positive_number) < \"pi%2F2\"\r\n" );
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document.write( "tan-1(0) = 0\r\n" );
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document.write( "\"-pi%2F2\" < tan-1(negative_number) < 0\r\n" );
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document.write( "Therefore in your problem:\r\n" );
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document.write( "sin[tan-1(-√3)]\r\n" );
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document.write( "ee first find the tan-1(-√3).\r\n" );
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document.write( "That asks the question:\r\n" );
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document.write( "\"What angle in the fourth quadrant taken in the interval (\"-pi%2F2\",0)\r\n" );
document.write( "has a tangent of -√3?\"\r\n" );
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document.write( "That brings to mind the special angle 60° or \"pi%2F3\", whose tangent is +√3.\r\n" );
document.write( "So we think of an angle in quadrant IV that has 60° for its referent angle,\r\n" );
document.write( "since angles in Q4 have negative tangents.\r\n" );
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document.write( "[We may think of 300° or \"5pi%2F3\", even though by convention it's actually\r\n" );
document.write( " measured clockwise as \"-pi%2F3\".\r\n" );
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document.write( "Anyway,\r\n" );
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document.write( "sin[tan-1(-√3)] = sin(\"-pi%2F3\") = \"-sqrt%283%29%2F2\".\r\n" );
document.write( "It's negative since the sine is negative in QIV.\r\n" );
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document.write( "Answer:  \"-sqrt%283%29%2F2\"\r\n" );
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document.write( "Edwin
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