document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1194933>Question 1194933</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use a half  -  angle identity to find the exact value of each expression.\r<BR>\n" );
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document.write( "5) tan 45°\r<BR>\n" );
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document.write( "6) sin 165°\r<BR>\n" );
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document.write( "7) sin  5π<BR>\n" );
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document.write( "        6\r<BR>\n" );
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document.write( "8.) cos 30°<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #827234 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</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=827234\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  <BR>\n" );
document.write( "Use a half - angle identity to find the exact value of each expression.\r<BR>\n" );
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document.write( "so, identities you need are:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28theta%2F2%29=sqrt%28%281-cos%28theta%29%29%2F2%29 ALIGN=MIDDLE  ALT=\"sin%28theta%2F2%29=sqrt%28%281-cos%28theta%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%28theta%2F2%29=sqrt%28%281%2Bcos%28theta%29%29%2F2%29 ALIGN=MIDDLE  ALT=\"cos%28theta%2F2%29=sqrt%28%281%2Bcos%28theta%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=tan%28theta%2F2%29=sin%28theta%29%2F%28cos%28theta%29+%2B+1%29 ALIGN=MIDDLE  ALT=\"tan%28theta%2F2%29=sin%28theta%29%2F%28cos%28theta%29+%2B+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "5) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan+45%C2%B0 ALIGN=MIDDLE  ALT=\"tan+45%C2%B0\"   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=theta%2F2=45 ALIGN=MIDDLE  ALT=\"theta%2F2=45\"   DISABLED_style= \"max-width:90%; height:auto;\" >° =><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta=90 ALIGN=MIDDLE  ALT=\"theta=90\"   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=tan%2845%29=sin%2890%29%2F%28cos%2890%29+%2B+1%29 ALIGN=MIDDLE  ALT=\"tan%2845%29=sin%2890%29%2F%28cos%2890%29+%2B+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >........<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%2890%29=1 ALIGN=MIDDLE  ALT=\"sin%2890%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%2890%29+=0 ALIGN=MIDDLE  ALT=\"cos%2890%29+=0\"   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=tan%2845%29=1%2F%280+%2B+1%29 ALIGN=MIDDLE  ALT=\"tan%2845%29=1%2F%280+%2B+1%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=tan+%2845%29=+1 ALIGN=MIDDLE  ALT=\"tan+%2845%29=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "6) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin+165 ALIGN=MIDDLE  ALT=\"sin+165\"   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=%28theta%2F2%29=165 ALIGN=MIDDLE  ALT=\"%28theta%2F2%29=165\"   DISABLED_style= \"max-width:90%; height:auto;\" >° =><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta=330 ALIGN=MIDDLE  ALT=\"theta=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=sin%28165%29=sqrt%28%281-cos%28330%29%29%2F2%29 ALIGN=MIDDLE  ALT=\"sin%28165%29=sqrt%28%281-cos%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=sin%28165%29=sqrt%28%281-sqrt%283%29%2F2%29%2F2%29 ALIGN=MIDDLE  ALT=\"sin%28165%29=sqrt%28%281-sqrt%283%29%2F2%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=sin%28165%29=sqrt%28%28%281%2F2%29+%282+-+sqrt%283%29%29%29%2F2%29 ALIGN=MIDDLE  ALT=\"sin%28165%29=sqrt%28%28%281%2F2%29+%282+-+sqrt%283%29%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=sin%28165%29=%28sqrt%283%29+-+1%29%2F%282+sqrt%282%29%29 ALIGN=MIDDLE  ALT=\"sin%28165%29=%28sqrt%283%29+-+1%29%2F%282+sqrt%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "7) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin+%285pi%2F6%29 ALIGN=MIDDLE  ALT=\"sin+%285pi%2F6%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=theta%2F2=%285pi%2F6%29 ALIGN=MIDDLE  ALT=\"theta%2F2=%285pi%2F6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > =><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta=2%285pi%2F6%29+=%285pi%2F3%29+ ALIGN=MIDDLE  ALT=\"theta=2%285pi%2F6%29+=%285pi%2F3%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%285pi%2F6%29=sqrt%28%281-cos%285pi%2F3%29%29%2F2%29 ALIGN=MIDDLE  ALT=\"sin%285pi%2F6%29=sqrt%28%281-cos%285pi%2F3%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=sin%285pi%2F6%29=sqrt%28%281%2F2%29%2F2%29 ALIGN=MIDDLE  ALT=\"sin%285pi%2F6%29=sqrt%28%281%2F2%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=sin%285pi%2F6%29=sqrt%281%2F4%29 ALIGN=MIDDLE  ALT=\"sin%285pi%2F6%29=sqrt%281%2F4%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%285pi%2F6%29=1%2F2 ALIGN=MIDDLE  ALT=\"sin%285pi%2F6%29=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "8.  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%2830%29 ALIGN=MIDDLE  ALT=\"cos%2830%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=theta%2F2=30 ALIGN=MIDDLE  ALT=\"theta%2F2=30\"   DISABLED_style= \"max-width:90%; height:auto;\" > =><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta=60+ ALIGN=MIDDLE  ALT=\"theta=60+\"   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%2830%29=sqrt%28%281%2Bcos%2860%29%29%2F2%29 ALIGN=MIDDLE  ALT=\"cos%2830%29=sqrt%28%281%2Bcos%2860%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%2830%29=sqrt%28%281%2B1%2F2%29%2F2%29 ALIGN=MIDDLE  ALT=\"cos%2830%29=sqrt%28%281%2B1%2F2%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%2830%29=sqrt%283%2F4%29 ALIGN=MIDDLE  ALT=\"cos%2830%29=sqrt%283%2F4%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%2830%29=sqrt%283%29%2F2 ALIGN=MIDDLE  ALT=\"cos%2830%29=sqrt%283%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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