document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1198721>Question 1198721</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given cos theta = -1/5 and tan theta < 0, find cot theta and sin theta. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #832551 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=832551\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
document.write( "\n" );
document.write( "Given: \r<BR>\n" );
document.write( "\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28+theta%29+=+-1%2F5 ALIGN=MIDDLE  ALT=\"cos%28+theta%29+=+-1%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan+%28theta%29+%3C+0 ALIGN=MIDDLE  ALT=\"tan+%28theta%29+%3C+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "find:\r<BR>\n" );
document.write( "\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cot+%28theta%29 ALIGN=MIDDLE  ALT=\"cot+%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin+%28theta%29 ALIGN=MIDDLE  ALT=\"sin+%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Start with the identity:\r<BR>\n" );
document.write( "\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%5E2%28+theta%29+=1-sin%5E2%28theta%29 ALIGN=MIDDLE  ALT=\"cos%5E2%28+theta%29+=1-sin%5E2%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28+theta%29+=+-1%2F5 ALIGN=MIDDLE  ALT=\"cos%28+theta%29+=+-1%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F5=1-sin%5E2%28theta%29 ALIGN=MIDDLE  ALT=\"-1%2F5=1-sin%5E2%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%5E2%28theta%29=1-1%2F5 ALIGN=MIDDLE  ALT=\"sin%5E2%28theta%29=1-1%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%5E2%28theta%29=4%2F5 ALIGN=MIDDLE  ALT=\"sin%5E2%28theta%29=4%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28theta%29 ALIGN=MIDDLE  ALT=\"sin%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=±<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%284%2F5%29 ALIGN=MIDDLE  ALT=\"sqrt%284%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28theta%29 ALIGN=MIDDLE  ALT=\"sin%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=±<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282sqrt%285%29%29%2F5 ALIGN=MIDDLE  ALT=\"%282sqrt%285%29%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan+%28theta%29+%3C+0 ALIGN=MIDDLE  ALT=\"tan+%28theta%29+%3C+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28theta%29=-%282sqrt%285%29%29%2F5 ALIGN=MIDDLE  ALT=\"sin%28theta%29=-%282sqrt%285%29%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "then\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%5E2%28+theta%29+=1-%28-%282sqrt%285%29%29%2F5%29%5E2 ALIGN=MIDDLE  ALT=\"cos%5E2%28+theta%29+=1-%28-%282sqrt%285%29%29%2F5%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%5E2%28+theta%29+=1%2F5 ALIGN=MIDDLE  ALT=\"cos%5E2%28+theta%29+=1%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28+theta%29 ALIGN=MIDDLE  ALT=\"cos%28+theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > =±<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%281%2F5%29 ALIGN=MIDDLE  ALT=\"sqrt%281%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28+theta%29+ ALIGN=MIDDLE  ALT=\"cos%28+theta%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >=±sqrt(5)/5}}}\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cot+%28theta%29=cos%28theta%29%2Fsin%28theta%29 ALIGN=MIDDLE  ALT=\"cot+%28theta%29=cos%28theta%29%2Fsin%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >...........since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan+%28theta%29%3C0+ ALIGN=MIDDLE  ALT=\"tan+%28theta%29%3C0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28theta%29=-%282sqrt%285%29%29%2F5 ALIGN=MIDDLE  ALT=\"sin%28theta%29=-%282sqrt%285%29%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, use positive solution for cos\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28+theta%29+=sqrt%285%29%2F5 ALIGN=MIDDLE  ALT=\"cos%28+theta%29+=sqrt%285%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "so,\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cot+%28theta%29=%28sqrt%285%29%2F5%29%2F%28-%282sqrt%285%29%29%2F5%29 ALIGN=MIDDLE  ALT=\"cot+%28theta%29=%28sqrt%285%29%2F5%29%2F%28-%282sqrt%285%29%29%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cot+%28theta%29=-1%2F2 ALIGN=MIDDLE  ALT=\"cot+%28theta%29=-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );