document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=790215>Question 790215</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do I find the exact values of all the angles between 0 rad and 2pi rad for which cos(x)=-square root 3 / 2? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #479095 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=479095\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The graph of <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;\" > looks like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28750%2C250%2C-0.5%2C7%2C-1.25%2C1.25%2Ccos%28x%29%29 ALIGN=MIDDLE  ALT=\"graph%28750%2C250%2C-0.5%2C7%2C-1.25%2C1.25%2Ccos%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Sine and cosine range from -1 to 1, and have a period of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2pi ALIGN=MIDDLE  ALT=\"2pi\"   DISABLED_style= \"max-width:90%; height:auto;\" > (4 quadrants).<BR>\n" );
document.write( "Over a period, they go full circle, up to 1, down to -1, and back.<BR>\n" );
document.write( "So, within a period, they go twice through any value other than the extremes, -1 and 1, once on the way up, and another time on the way down, and in different quadrants.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28x%29%3C0 ALIGN=MIDDLE  ALT=\"cos%28x%29%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" > in quadrants II (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2F2%3Cx%3C=pi ALIGN=MIDDLE  ALT=\"pi%2F2%3Cx%3C=pi\"   DISABLED_style= \"max-width:90%; height:auto;\" >), and III (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%3C=x%3C3pi%2F2 ALIGN=MIDDLE  ALT=\"pi%3C=x%3C3pi%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so there will be a solution for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28x%29=-sqrt%283%29%2F2 ALIGN=MIDDLE  ALT=\"cos%28x%29=-sqrt%283%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > in each of those quadrants.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28pi%2F6%29=sqrt%283%29%2F2 ALIGN=MIDDLE  ALT=\"cos%28pi%2F6%29=sqrt%283%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is one of 5 numbers that you will see in many problems about trigonometric function values.<BR>\n" );
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;\" > is the opposite value, corresponding to the supplementary angle, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi-pi%2F6=highlight%285pi%2F6%29 ALIGN=MIDDLE  ALT=\"pi-pi%2F6=highlight%285pi%2F6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2Bpi%2F6=highlight%287pi%2F6%29 ALIGN=MIDDLE  ALT=\"pi%2Bpi%2F6=highlight%287pi%2F6%29\"   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-1.2%2C1.2%2C-1.2%2C1.2%2Cgrid%280%29%2C%0D%0Acircle%280%2C0%2C1%29%2Carrow%280%2C0%2C1.17%2C0.675%29%2Carrow%280%2C0%2C-1.17%2C0.675%29%2Carrow%280%2C0%2C-1.17%2C-0.675%29%2C%0D%0Acircle%280.866%2C0.5%2C0.03%29%2Ccircle%28-0.866%2C0.5%2C0.03%29%2Ccircle%28-0.866%2C-0.5%2C0.03%29%2C%0D%0Alocate%280.4%2C0.28%2Cpi%2F6%29%2Clocate%280.92%2C0.55%2CA%29%2C%0D%0Alocate%28-0.5%2C0.28%2Cpi%2F6%29%2Clocate%28-1%2C0.55%2CB%29%2C%0D%0Alocate%28-0.52%2C0.02%2Cpi%2F6%29%2Clocate%28-1%2C-0.45%2CC%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Points <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22A+%28%22 ALIGN=MIDDLE  ALT=\"%22A+%28%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><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;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22%2C%22 ALIGN=MIDDLE  ALT=\"%22%2C%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><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;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22%29%22 ALIGN=MIDDLE  ALT=\"%22%29%22\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22B+%28%22 ALIGN=MIDDLE  ALT=\"%22B+%28%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><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;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22%2C%22 ALIGN=MIDDLE  ALT=\"%22%2C%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><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;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22%29%22 ALIGN=MIDDLE  ALT=\"%22%29%22\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22C+%28%22 ALIGN=MIDDLE  ALT=\"%22C+%28%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><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;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22%2C%22 ALIGN=MIDDLE  ALT=\"%22%2C%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><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;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22%29%22 ALIGN=MIDDLE  ALT=\"%22%29%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > are circled<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28pi-pi%2F6%29=cos%285pi%2F6%29=-sqrt%283%29%2F2 ALIGN=MIDDLE  ALT=\"cos%28pi-pi%2F6%29=cos%285pi%2F6%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%28pi%2Bpi%2F6%29=cos%287pi%2F6%29=-sqrt%283%29%2F2 ALIGN=MIDDLE  ALT=\"cos%28pi%2Bpi%2F6%29=cos%287pi%2F6%29=-sqrt%283%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "EXTRA:<BR>\n" );
document.write( "The 5 trigonometric function values that you will often see:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%280%29=highlight%281%29=sin%28pi%2F2%29 ALIGN=MIDDLE  ALT=\"cos%280%29=highlight%281%29=sin%28pi%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28pi%2F6%29=highlight%28sqrt%283%29%2F2%29=sin%28pi%2F3%29 ALIGN=MIDDLE  ALT=\"cos%28pi%2F6%29=highlight%28sqrt%283%29%2F2%29=sin%28pi%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28pi%2F4%29=highlight%28sqrt%282%29%2F2%29=sin%28pi%2F4%29 ALIGN=MIDDLE  ALT=\"cos%28pi%2F4%29=highlight%28sqrt%282%29%2F2%29=sin%28pi%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=cos%28pi%2F3%29=highlight%281%2F2%29=sin%28pi%2F6%29 ALIGN=MIDDLE  ALT=\"cos%28pi%2F3%29=highlight%281%2F2%29=sin%28pi%2F6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28pi%2F2%29=highlight%280%29=sin%280%29 ALIGN=MIDDLE  ALT=\"cos%28pi%2F2%29=highlight%280%29=sin%280%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );