document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1139293>Question 1139293</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help finding the exact values\r<BR>\n" );
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document.write( "Use a double-angle identity to find the exact value of each expression.\r<BR>\n" );
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document.write( "1. sin 120°\r<BR>\n" );
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document.write( "2. tan 60°\r<BR>\n" );
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document.write( "3. cos 4π/3\r<BR>\n" );
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document.write( "4. sin 5π/3''.<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 #757086 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=757086\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "Use a double-angle identity to find the exact value of each expression. \r<BR>\n" );
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document.write( "1.<BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28+120+%29 ALIGN=MIDDLE  ALT=\"sin%28+120+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >..........use identity <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28+2a%29+=+2sin%28a%29+cos%28a%29 ALIGN=MIDDLE  ALT=\"sin%28+2a%29+=+2sin%28a%29+cos%28a%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%28+2%2A60%29 ALIGN=MIDDLE  ALT=\"sin%28+2%2A60%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=2sin%2860%29+cos%2860%29 ALIGN=MIDDLE  ALT=\"2sin%2860%29+cos%2860%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=2sqrt%283%29%2F2%2A%281%2F2%29 ALIGN=MIDDLE  ALT=\"2sqrt%283%29%2F2%2A%281%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=cross%282%29sqrt%283%29%2F2%2A%281%2Fcross%282%29%29 ALIGN=MIDDLE  ALT=\"cross%282%29sqrt%283%29%2F2%2A%281%2Fcross%282%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=sqrt%283%29%2F2 ALIGN=MIDDLE  ALT=\"sqrt%283%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "2. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan+%2860%29 ALIGN=MIDDLE  ALT=\"tan+%2860%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+%282%2A30%29+ ALIGN=MIDDLE  ALT=\"tan+%282%2A30%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+%282%2A30%29+%2Fcos%282%2A30%29 ALIGN=MIDDLE  ALT=\"sin+%282%2A30%29+%2Fcos%282%2A30%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.........................<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28+2a%29+=+2sin%28a%29+cos%28a%29 ALIGN=MIDDLE  ALT=\"sin%28+2a%29+=+2sin%28a%29+cos%28a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos+%282a%29+=+cos%5E2%28a%29+-+sin%5E2%28a%29+ ALIGN=MIDDLE  ALT=\"cos+%282a%29+=+cos%5E2%28a%29+-+sin%5E2%28a%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=%282sin%2830%29+cos%2830%29%29%2F%28cos%5E2%2830%29+-+sin%5E2%2830%29+%29 ALIGN=MIDDLE  ALT=\"%282sin%2830%29+cos%2830%29%29%2F%28cos%5E2%2830%29+-+sin%5E2%2830%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=%282%281%2F2%29+%28sqrt%283%29%2F2%29%29%2F%283%2F4+-+1%2F4+%29 ALIGN=MIDDLE  ALT=\"%282%281%2F2%29+%28sqrt%283%29%2F2%29%29%2F%283%2F4+-+1%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=%281%2A+%28sqrt%283%29%2F2%29%29%2F%282%2F4+%29 ALIGN=MIDDLE  ALT=\"%281%2A+%28sqrt%283%29%2F2%29%29%2F%282%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=4sqrt%283%29%2F4 ALIGN=MIDDLE  ALT=\"4sqrt%283%29%2F4\"   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=sqrt%283%29 ALIGN=MIDDLE  ALT=\"sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "3.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+cos+%284pi%2F3+%29 ALIGN=MIDDLE  ALT=\"+cos+%284pi%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=cos+%282%2A%282pi%2F3+%29%29 ALIGN=MIDDLE  ALT=\"cos+%282%2A%282pi%2F3+%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%5E2%282pi%2F3%29+-+sin%5E2%282pi%2F3%29+ ALIGN=MIDDLE  ALT=\"cos%5E2%282pi%2F3%29+-+sin%5E2%282pi%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=1%2F4-3%2F4 ALIGN=MIDDLE  ALT=\"1%2F4-3%2F4\"   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=-2%2F4 ALIGN=MIDDLE  ALT=\"-2%2F4\"   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 ALIGN=MIDDLE  ALT=\"-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "4. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28+5pi%2F3+%29 ALIGN=MIDDLE  ALT=\"sin%28+5pi%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%28+3pi%2F3+%2B2pi%2F3%29 ALIGN=MIDDLE  ALT=\"sin%28+3pi%2F3+%2B2pi%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%28+pi+%2B2pi%2F3%29 ALIGN=MIDDLE  ALT=\"sin%28+pi+%2B2pi%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >..........use <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin+%28a+%2B+b%29+=+sin+%28a%29+cos%28+b%29+%2B+sin+%28b%29+cos+%28a%29 ALIGN=MIDDLE  ALT=\"sin+%28a+%2B+b%29+=+sin+%28a%29+cos%28+b%29+%2B+sin+%28b%29+cos+%28a%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%28+pi%29cos%282pi%2F3%29+%2Bsin%282pi%2F3%29cos%28pi%29 ALIGN=MIDDLE  ALT=\"sin%28+pi%29cos%282pi%2F3%29+%2Bsin%282pi%2F3%29cos%28pi%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=0%2A%28-1%2F2%29+%2B%28sqrt%283%29%2F2%29%28-1%29 ALIGN=MIDDLE  ALT=\"0%2A%28-1%2F2%29+%2B%28sqrt%283%29%2F2%29%28-1%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=-sqrt%283%29%2F2 ALIGN=MIDDLE  ALT=\"-sqrt%283%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );