document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=970477>Question 970477</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Evaluate cos[arctan(-5/12)].  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #854526 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(53875)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=854526\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "Evaluate cos[arctan(-5/12)].<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;In the post by @lwsshak3 the answer is incorrect and reasoning is also incorrect.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;See below my correct solution.\r<BR>\n" );
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document.write( "Function arctan has values in the interval (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-pi%2F2 ALIGN=MIDDLE  ALT=\"-pi%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2F2 ALIGN=MIDDLE  ALT=\"pi%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >).\r<BR>\n" );
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document.write( "Therefore, the problem asks to evaluate cos(x), given that 'x' is in the fourth quadrant<BR>\n" );
document.write( "(not in the second quadrant, as @lwsshak3 mistakenly assumes) and tan(x) = -5/12.\r<BR>\n" );
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document.write( "So, let x=angle in QIV whose tan is (-5/12)<BR>\n" );
document.write( "tan(x) = (-5/12) (working with a (5-12-13) right triangle in quadrant IV)<BR>\n" );
document.write( "cosine is positive in QIV; therefore<BR>\n" );
document.write( "cos[arctan(-5/12)] = cos(x) = 12/13.\r<BR>\n" );
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document.write( "<U>ANSWER</U>.  cos[arctan(-5/12)] = 12/13.\r<BR>\n" );
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document.write( "Solved correctly.\r<BR>\n" );
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