document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1159668>Question 1159668</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use half-angle formulas to find the exact values.<BR>\n" );
document.write( "cos 165°\r<BR>\n" );
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document.write( "I got <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282%2B%7B%7B%7B%28sqrt3%29 ALIGN=MIDDLE  ALT=\"sqrt%282%2B%7B%7B%7B%28sqrt3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >/2 which is wrong.\r<BR>\n" );
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document.write( "This is my work:\r<BR>\n" );
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document.write( "165=θ/2<BR>\n" );
document.write( "330=  θ\r<BR>\n" );
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document.write( "cos  θ/2= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%281%2Bcos+%CE%B8%29 ALIGN=MIDDLE  ALT=\"sqrt%281%2Bcos+%CE%B8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >/2= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%281%2B%28%7B%7B%7Bsqrt%283%29 ALIGN=MIDDLE  ALT=\"sqrt%28%281%2B%28%7B%7B%7Bsqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >/2)/2)}}}}}}= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282%2B%7B%7B%7B%28sqrt3%29 ALIGN=MIDDLE  ALT=\"sqrt%282%2B%7B%7B%7B%28sqrt3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >}}}/2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #782684 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=782684\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28A%2F2%29 ALIGN=MIDDLE  ALT=\"cos%28A%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=± <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%281%2Bcos%28A%29%29%2F2%29 ALIGN=MIDDLE  ALT=\"sqrt%28%281%2Bcos%28A%29%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%2F2 ALIGN=MIDDLE  ALT=\"A%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is in the first or fourth quadrants, the formula uses the positive case:<BR>\n" );
document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%2F2+ ALIGN=MIDDLE  ALT=\"A%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >is in the second or third quadrants, the formula uses the negative case:\r<BR>\n" );
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document.write( "in your case angle is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%2F2=165 ALIGN=MIDDLE  ALT=\"A%2F2=165\"   DISABLED_style= \"max-width:90%; height:auto;\" >°-> the second quadrant\r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%2F2=165 ALIGN=MIDDLE  ALT=\"A%2F2=165\"   DISABLED_style= \"max-width:90%; height:auto;\" >°, -><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=330 ALIGN=MIDDLE  ALT=\"A=330\"   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%28165%29=-sqrt%28%281%2Bcos%28330%29%29%2F2%29 ALIGN=MIDDLE  ALT=\"cos%28165%29=-sqrt%28%281%2Bcos%28330%29%29%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=cos%28165%29=-sqrt%281%2F2+%281+%2B+sqrt%283%29%2F2%29%29 ALIGN=MIDDLE  ALT=\"cos%28165%29=-sqrt%281%2F2+%281+%2B+sqrt%283%29%2F2%29%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%28165%29=-sqrt%28+%281+%2B+sqrt%283%29%2F4%29%29 ALIGN=MIDDLE  ALT=\"cos%28165%29=-sqrt%28+%281+%2B+sqrt%283%29%2F4%29%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%28165%29=-sqrt%282+%2B+sqrt%283%29%29%2F2 ALIGN=MIDDLE  ALT=\"cos%28165%29=-sqrt%282+%2B+sqrt%283%29%29%2F2\"   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%28165%29=-%281+%2B+sqrt%283%29%29%2F%282sqrt%282%29%29 ALIGN=MIDDLE  ALT=\"cos%28165%29=-%281+%2B+sqrt%283%29%29%2F%282sqrt%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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