document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=865985>Question 865985</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Question: Find all angles theta (I don't have a symbol for that) in radians on the interval [0,4pi] such that cos(theta) = 1/2.\r<BR>\n" );
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document.write( "I think I have to set a up graph from 0 to 4pi and draw a wavy line and determine at what points x crosses y=1/2. It that correct? How do I do that? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #522012 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=522012\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Plot <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+theta+ ALIGN=MIDDLE  ALT=\"+theta+\"   DISABLED_style= \"max-width:90%; height:auto;\" > on the horizontal axis and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+cos%28+theta+%29+ ALIGN=MIDDLE  ALT=\"+cos%28+theta+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > on the vertical axis.<BR>\n" );
document.write( "----------------------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4%2Api+ ALIGN=MIDDLE  ALT=\"+4%2Api+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is two cycles of the cos wave.<BR>\n" );
document.write( "The cos starts out at +1, then goes to zero,<BR>\n" );
document.write( "then to -1, then back to zero ( 1 complete cycle )<BR>\n" );
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document.write( "The only places where the cos is positive is<BR>\n" );
document.write( "the 1st quadrant and the 4th quadrant.<BR>\n" );
document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+cos%28+theta+%29+=+1%2F2+ ALIGN=MIDDLE  ALT=\"+cos%28+theta+%29+=+1%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+arc+cos%28+1%2F2+%29+=+pi%2F3+ ALIGN=MIDDLE  ALT=\"+arc+cos%28+1%2F2+%29+=+pi%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and, also<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+arc+cos%28+1%2F2+%29+=++%285%2Api%29+%2F+3+ ALIGN=MIDDLE  ALT=\"+arc+cos%28+1%2F2+%29+=++%285%2Api%29+%2F+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--------------------------------<BR>\n" );
document.write( "To get all the angles from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0+ ALIGN=MIDDLE  ALT=\"+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4%2Api+ ALIGN=MIDDLE  ALT=\"+4%2Api+\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "You just have to add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%2Api+ ALIGN=MIDDLE  ALT=\"+2%2Api+\"   DISABLED_style= \"max-width:90%; height:auto;\" > to these<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+pi%2F3+%2B+2%2Api+=+%28+7%2Api+%29%2F3+ ALIGN=MIDDLE  ALT=\"+pi%2F3+%2B+2%2Api+=+%28+7%2Api+%29%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+5%2Api+%29%2F3+%2B+2%2Api+=+%28+11%2Api+%29%2F3+ ALIGN=MIDDLE  ALT=\"+%28+5%2Api+%29%2F3+%2B+2%2Api+=+%28+11%2Api+%29%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--------------------------------<BR>\n" );
document.write( "So, the answers are:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+pi%2F3+ ALIGN=MIDDLE  ALT=\"+pi%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+5%2Api+%29+%2F+3+ ALIGN=MIDDLE  ALT=\"+%28+5%2Api+%29+%2F+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+7%2Api+%29+%2F+3+ ALIGN=MIDDLE  ALT=\"+%28+7%2Api+%29+%2F+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+11%2Api+%29+%2F+3+ ALIGN=MIDDLE  ALT=\"+%28+11%2Api+%29+%2F+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---------------------------------<BR>\n" );
document.write( "Here's the plot:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+600%2C+400%2C+-pi%2F2%2C+4%2Api%2C+-2%2C+2%2C+cos%28x%29%2C+.5+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+400%2C+-pi%2F2%2C+4%2Api%2C+-2%2C+2%2C+cos%28x%29%2C+.5+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );