document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=149721>Question 149721</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the exact value of cot(-pie/6) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #109860 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=109860\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cot%28-pi%2F6%29 ALIGN=MIDDLE  ALT=\"cot%28-pi%2F6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given expression.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Ftan%28-pi%2F6%29 ALIGN=MIDDLE  ALT=\"1%2Ftan%28-pi%2F6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite the cotangent in terms of tangent.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28-tan%28pi%2F6%29%29 ALIGN=MIDDLE  ALT=\"1%2F%28-tan%28pi%2F6%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Use the identity <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28-u%29=-tan%28u%29 ALIGN=MIDDLE  ALT=\"tan%28-u%29=-tan%28u%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to rewrite the expression.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2Ftan%28pi%2F6%29 ALIGN=MIDDLE  ALT=\"-1%2Ftan%28pi%2F6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F%28%28sin%28pi%2F6%29%29%2F%28cos%28pi%2F6%29%29%29 ALIGN=MIDDLE  ALT=\"-1%2F%28%28sin%28pi%2F6%29%29%2F%28cos%28pi%2F6%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite the tangent function in terms of sine and cosine.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%28cos%28pi%2F6%29%2Fsin%28pi%2F6%29%29 ALIGN=MIDDLE  ALT=\"-1%28cos%28pi%2F6%29%2Fsin%28pi%2F6%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply -1 by the reciprocal of the dividing fraction.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-cos%28pi%2F6%29%2Fsin%28pi%2F6%29 ALIGN=MIDDLE  ALT=\"-cos%28pi%2F6%29%2Fsin%28pi%2F6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply.\r<BR>\n" );
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document.write( "Now, let's reference the unit circle\r<BR>\n" );
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document.write( "From the unit circle, we can see that at the angle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2F6 ALIGN=MIDDLE  ALT=\"pi%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >, there is a point on the unit circle <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(\frac{\sqrt{3}}{2},\frac{1}{2}\right)\">. So this tells us that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28pi%2F6%29=sqrt%283%29%2F2 ALIGN=MIDDLE  ALT=\"cos%28pi%2F6%29=sqrt%283%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28pi%2F6%29=1%2F2 ALIGN=MIDDLE  ALT=\"sin%28pi%2F6%29=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-cos%28pi%2F6%29%2Fsin%28pi%2F6%29 ALIGN=MIDDLE  ALT=\"-cos%28pi%2F6%29%2Fsin%28pi%2F6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > then becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28sqrt%283%29%2F2%29%2F%281%2F2%29 ALIGN=MIDDLE  ALT=\"-%28sqrt%283%29%2F2%29%2F%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28sqrt%283%29%2F2%29%2A%282%2F1%29 ALIGN=MIDDLE  ALT=\"-%28sqrt%283%29%2F2%29%2A%282%2F1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the first fraction by the reciprocal of the second fraction.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28sqrt%283%29%2Fcross%282%29%29%2A%28cross%282%29%2F1%29 ALIGN=MIDDLE  ALT=\"-%28sqrt%283%29%2Fcross%282%29%29%2A%28cross%282%29%2F1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Cancel like terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-sqrt%283%29 ALIGN=MIDDLE  ALT=\"-sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply and simplify.\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cot%28-pi%2F6%29=-sqrt%283%29 ALIGN=MIDDLE  ALT=\"cot%28-pi%2F6%29=-sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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