document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1198723>Question 1198723</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given cot theta =-2 and csc theta < 0, find sin theta and sec theta </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #832549 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=832549\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "Given: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cot%28theta%29=-2 ALIGN=MIDDLE  ALT=\"cot%28theta%29=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=csc%28theta%29+%3C+0 ALIGN=MIDDLE  ALT=\"csc%28theta%29+%3C+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "find:\r<BR>\n" );
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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;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sec%28+theta%29 ALIGN=MIDDLE  ALT=\"sec%28+theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Start with the identity:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Bcot%5E2%28theta%29=csc%5E2%28theta%29 ALIGN=MIDDLE  ALT=\"1%2Bcot%5E2%28theta%29=csc%5E2%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Substitute \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cot%5E2%28theta%29=%28-2%29%5E2 ALIGN=MIDDLE  ALT=\"cot%5E2%28theta%29=%28-2%29%5E2\"   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=1%2B%28-2%29%5E2=csc%5E2%28theta%29 ALIGN=MIDDLE  ALT=\"1%2B%28-2%29%5E2=csc%5E2%28theta%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=5=csc%5E2%28theta%29 ALIGN=MIDDLE  ALT=\"5=csc%5E2%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Substitute \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=csc%5E2%28theta%29=1%2Fsin%5E2%28theta%29 ALIGN=MIDDLE  ALT=\"csc%5E2%28theta%29=1%2Fsin%5E2%28theta%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=5=1%2Fsin%5E2%28theta%29 ALIGN=MIDDLE  ALT=\"5=1%2Fsin%5E2%28theta%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=sin%5E2%28theta%29=1%2F5 ALIGN=MIDDLE  ALT=\"sin%5E2%28theta%29=1%2F5\"   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=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%281%2F5%29 ALIGN=MIDDLE  ALT=\"sqrt%281%2F5%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=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%285%29%2F5 ALIGN=MIDDLE  ALT=\"sqrt%285%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "use negative solution since <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;\" > negative in  Q III and  Q IV\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sec%28+theta%29=1%2Fcos%28theta%29 ALIGN=MIDDLE  ALT=\"sec%28+theta%29=1%2Fcos%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "use <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%5E2%28theta%29=1-+sin%5E2%28theta%29 ALIGN=MIDDLE  ALT=\"cos%5E2%28theta%29=1-+sin%5E2%28theta%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=cos%5E2%28theta%29=1-+1%2F5 ALIGN=MIDDLE  ALT=\"cos%5E2%28theta%29=1-+1%2F5\"   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=cos%5E2%28theta%29=4%2F5 ALIGN=MIDDLE  ALT=\"cos%5E2%28theta%29=4%2F5\"   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=cos%28theta%29=sqrt%284%2F5%29 ALIGN=MIDDLE  ALT=\"cos%28theta%29=sqrt%284%2F5%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=cos%28theta%29 ALIGN=MIDDLE  ALT=\"cos%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=±<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282+sqrt%285%29%29%2F5 ALIGN=MIDDLE  ALT=\"%282+sqrt%285%29%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "then\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sec%28+theta%29=1%2F%28%282+sqrt%285%29%29%2F5%29=sqrt%285%29%2F2 ALIGN=MIDDLE  ALT=\"sec%28+theta%29=1%2F%28%282+sqrt%285%29%29%2F5%29=sqrt%285%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sec%28+theta%29=1%2F%28-%282+sqrt%285%29%29%2F5%29=-sqrt%285%29%2F2 ALIGN=MIDDLE  ALT=\"sec%28+theta%29=1%2F%28-%282+sqrt%285%29%29%2F5%29=-sqrt%285%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "since <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;\" > and <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;\" > negative in  Q III and  Q IV\r<BR>\n" );
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document.write( "then, \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sec%28+theta%29=sqrt%285%29%2F2 ALIGN=MIDDLE  ALT=\"sec%28+theta%29=sqrt%285%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > in  Q IV\r<BR>\n" );
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document.write( "and\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sec%28+theta%29=-sqrt%285%29%2F2 ALIGN=MIDDLE  ALT=\"sec%28+theta%29=-sqrt%285%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > in  Q III\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );