document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=873813>Question 873813</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do I solve this?	Use the exact values of the sine and cosine of 2&#960;/3 and &#960; /4, and the angle sum identity for sine, to find the exact value of sin(11 &#960; /12). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #527140 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=527140\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The angle sum identity for sine is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28A%2BB%29=sin%28A%29%2Acos%28B%29%2Bcos%28A%29%2Asin%28B%29 ALIGN=MIDDLE  ALT=\"sin%28A%2BB%29=sin%28A%29%2Acos%28B%29%2Bcos%28A%29%2Asin%28B%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2pi%2F3%2Bpi%2F4=8pi%2F12%2B3pi%2F12=11pi%2F12 ALIGN=MIDDLE  ALT=\"2pi%2F3%2Bpi%2F4=8pi%2F12%2B3pi%2F12=11pi%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "you can use the angle sum identity (above),<BR>\n" );
document.write( "and the values for sine and cosine of <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;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2F4 ALIGN=MIDDLE  ALT=\"pi%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "to find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%2811pi%2F12%29=sin%282pi%2F3%2Bpi%2F4%29 ALIGN=MIDDLE  ALT=\"sin%2811pi%2F12%29=sin%282pi%2F3%2Bpi%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28pi%2F4%29 ALIGN=MIDDLE  ALT=\"sin%28pi%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28pi%2F4%29 ALIGN=MIDDLE  ALT=\"cos%28pi%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > are easy. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2F4 ALIGN=MIDDLE  ALT=\"pi%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=45%5Eo ALIGN=MIDDLE  ALT=\"45%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28pi%2F4%29=cos%28pi%2F4%29=sqrt%282%29%2F2 ALIGN=MIDDLE  ALT=\"sin%28pi%2F4%29=cos%28pi%2F4%29=sqrt%282%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-0.8%2C0.2%2C-0.2%2C0.8%2C%0D%0Atriangle%280%2C0%2C-.707%2C0%2C0%2C0.707%29%2C%0D%0Arectangle%280%2C0%2C-0.05%2C0.05%29%2C%0D%0Aarc%28-0.707%2C0%2C0.4%2C0.4%2C-45%2C0%29%2C%0D%0Aarc%280%2C0.707%2C0.4%2C0.4%2C-270%2C-225%29%2C%0D%0Alocate%28-0.36%2C-0.02%2Csqrt%282%29%2F2%29%2Clocate%280.03%2C0.38%2Csqrt%282%29%2F2%29%2C%0D%0Alocate%28-0.34%2C0.36%2C1%29%2Clocate%28-0.58%2C0.12%2Cpi%2F4%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<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;\" > is a little harder because it is in quadrant II.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-1.2%2C1.2%2C-1.2%2C1.2%2C%0D%0Agrid%280%29%2Ccircle%280%2C0%2C1%29%2C%0D%0Aarrow%280%2C0%2C0.65%2C1.126%29%2Carrow%280%2C0%2C-0.65%2C1.126%29%2C%0D%0Ared%28arc%280%2C0%2C0.8%2C0.8%2C-60%2C0%29%29%2Clocate%280.18%2C0.3%2Cred%28pi%2F3%29%29%2C%0D%0Ared%28arc%280%2C0%2C0.8%2C0.8%2C-180%2C-120%29%29%2Clocate%28-0.24%2C0.3%2Cred%28pi%2F3%29%29%2C%0D%0Ablue%28arc%280%2C0%2C1.5%2C1.5%2C-120%2C0%29%29%2Clocate%280.45%2C0.45%2Cblue%282pi%2F3%29%29%2C%0D%0Ared%28circle%280.5%2C0.866%2C0.02%29%29%2Clocate%280.58%2C1.03%2Cred%28P%281%2F2%2Csqrt%283%29%2F2%29%29%29%0D%0A%29 ALIGN=MIDDLE   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%282pi%2F3%29=sin%28pi-2pi%2F3%29=sin%28pi%2F3%29=sqrt%283%29%2F2 ALIGN=MIDDLE  ALT=\"sin%282pi%2F3%29=sin%28pi-2pi%2F3%29=sin%28pi%2F3%29=sqrt%283%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%282pi%2F3%29=-cos%28pi-2pi%2F3%29=-cos%28pi%2F3%29=-1%2F2 ALIGN=MIDDLE  ALT=\"cos%282pi%2F3%29=-cos%28pi-2pi%2F3%29=-cos%28pi%2F3%29=-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "So, applying <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28A%2BB%29=sin%28A%29%2Acos%28B%29%2Bcos%28A%29%2Asin%28B%29 ALIGN=MIDDLE  ALT=\"sin%28A%2BB%29=sin%28A%29%2Acos%28B%29%2Bcos%28A%29%2Asin%28B%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=2pi%2F3 ALIGN=MIDDLE  ALT=\"A=2pi%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=pi%2F4 ALIGN=MIDDLE  ALT=\"B=pi%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%2811pi%2F12%29=sin%282pi%2F3%2Bpi%2F4%29=sin%282pi%2F3%29%2Acos%28pi%2F4%29%2Bcos%282pi%2F3%29%2Asin%28pi%2F4%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%283%29%2F2%29%28sqrt%282%29%2F2%29%2B%28-1%2F2%29%28sqrt%282%29%2F2%29=sqrt%283%29%2Asqrt%282%29%2F4-sqrt%282%29%2F4 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "That could be \"simplified\" different ways:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283%29%2Asqrt%282%29%2F4-sqrt%282%29%2F4=highlight%28%28sqrt%286%29-sqrt%282%29%29%2F4%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283%29%2Asqrt%282%29%2F4-sqrt%282%29%2F4=highlight%28%28sqrt%283%29-1%29sqrt%282%29%2F4%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Those expressions are the exact value of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%2811pi%2F12%29 ALIGN=MIDDLE  ALT=\"sin%2811pi%2F12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );