document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=169169>Question 169169</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the exact value of the expression. sec^-1(-2) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #124747 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=124747\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=sec%5E%28-1%29%28-2%29 ALIGN=MIDDLE  ALT=\"x=sec%5E%28-1%29%28-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sec%28x%29=-2 ALIGN=MIDDLE  ALT=\"sec%28x%29=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > which further tells \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sec%28x%29=-2 ALIGN=MIDDLE  ALT=\"sec%28x%29=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fcos%28x%29=-2 ALIGN=MIDDLE  ALT=\"1%2Fcos%28x%29=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Replace secant with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fcosine ALIGN=MIDDLE  ALT=\"1%2Fcosine\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Take note that cosine is negative (since 1 divided by a negative number is negative). This means that the angle MUST be in either the 2nd or 3rd quadrants.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1=-2cos%28x%29 ALIGN=MIDDLE  ALT=\"1=-2cos%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28x%29 ALIGN=MIDDLE  ALT=\"cos%28x%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=-1%2F2=cos%28x%29 ALIGN=MIDDLE  ALT=\"-1%2F2=cos%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by -2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=arccos%28-1%2F2%29=x ALIGN=MIDDLE  ALT=\"arccos%28-1%2F2%29=x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the arccosine (or inverse cosine) of both sides to isolate x\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-pi%2F3 ALIGN=MIDDLE  ALT=\"x=-pi%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2pi%2F3 ALIGN=MIDDLE  ALT=\"x=2pi%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the arccosine of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F2 ALIGN=MIDDLE  ALT=\"-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-pi%2F3 ALIGN=MIDDLE  ALT=\"-pi%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2pi%2F3 ALIGN=MIDDLE  ALT=\"2pi%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since it was stated above that the angle had to be in quadrants 2 or 3, this means that we can ignore <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-pi%2F3 ALIGN=MIDDLE  ALT=\"x=-pi%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2pi%2F3 ALIGN=MIDDLE  ALT=\"x=2pi%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > which means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sec%5E%28-1%29%28-2%29=2pi%2F3 ALIGN=MIDDLE  ALT=\"sec%5E%28-1%29%28-2%29=2pi%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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