document.write( "Question 970477: Evaluate cos[arctan(-5/12)]. \n" ); document.write( "
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\n" ); document.write( "Evaluate cos[arctan(-5/12)].
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\n" ); document.write( "\n" ); document.write( "Function arctan has values in the interval (\"-pi%2F2\",\"pi%2F2\").\r
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\n" ); document.write( "\n" ); document.write( "Therefore, the problem asks to evaluate cos(x), given that 'x' is in the fourth quadrant
\n" ); document.write( "and tan(x) = -5/12.\r
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\n" ); document.write( "\n" ); document.write( "So, let x=angle in QIV whose tan is (-5/12)
\n" ); document.write( "tan(x) = (-5/12) (working with a (5-12-13) right triangle in quadrant IV)
\n" ); document.write( "cosine is positive in QIV; therefore
\n" ); document.write( "cos[arctan(-5/12)] = cos(x) = 12/13.\r
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\n" ); document.write( "\n" ); document.write( "ANSWER. cos[arctan(-5/12)] = 12/13.\r
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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