document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=609385>Question 609385</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do you solve sin(x/2)-cosx=0 with a restriction of [0,2pi)? We are supposed to be using the half angle formula... </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #449605 by </B><A HREF=/tutors/aboutme.mpl?userid=Barbazzo><B>Barbazzo(2)</B></A><img src=\"/images/stars/iconNewId_16x16.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Barbazzo><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=449605\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos+x-sin%28x%2F2%29+=+0 ALIGN=MIDDLE  ALT=\"cos+x-sin%28x%2F2%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Transform Cos into Sin using Double Angle Identity: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%282u%29+=+1-2sin%5E2%28u%29 ALIGN=MIDDLE  ALT=\"cos%282u%29+=+1-2sin%5E2%28u%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u+=+x%2F2 ALIGN=MIDDLE  ALT=\"u+=+x%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28x%29+=+1-2sin%5E2%28x%2F2%29 ALIGN=MIDDLE  ALT=\"cos%28x%29+=+1-2sin%5E2%28x%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=1-2sin%5E2%28x%2F2%29+-+sin%28x%2F2%29+=+0 ALIGN=MIDDLE  ALT=\"1-2sin%5E2%28x%2F2%29+-+sin%28x%2F2%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2sin%5E2%28x%2F2%29-sin%28x%2F2%29%2B1+=+0 ALIGN=MIDDLE  ALT=\"-2sin%5E2%28x%2F2%29-sin%28x%2F2%29%2B1+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2sin%5E2%28x%2F2%29%2Bsin%28x%2F2%29-1+=+0 ALIGN=MIDDLE  ALT=\"2sin%5E2%28x%2F2%29%2Bsin%28x%2F2%29-1+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Factor: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sin%28x%2F2%29%2B1%29%282sin%28x%2F2%29-1%29+=+0 ALIGN=MIDDLE  ALT=\"%28sin%28x%2F2%29%2B1%29%282sin%28x%2F2%29-1%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Split into two equations:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28x%2F2%29%2B1+=+0 ALIGN=MIDDLE  ALT=\"sin%28x%2F2%29%2B1+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2sin%28x%2F2%29-1+=+0 ALIGN=MIDDLE  ALT=\"2sin%28x%2F2%29-1+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "For <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28x%2F2%29%2B1+=+0 ALIGN=MIDDLE  ALT=\"sin%28x%2F2%29%2B1+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28x%2F2%29+=+-1 ALIGN=MIDDLE  ALT=\"sin%28x%2F2%29+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Take the inverse Sin:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F2+=+2n%2Api-pi%2F2 ALIGN=MIDDLE  ALT=\"x%2F2+=+2n%2Api-pi%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, where n is an integer<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+4n%2Api-pi ALIGN=MIDDLE  ALT=\"x+=+4n%2Api-pi\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so no value of n is within the restriction 0 to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2pi ALIGN=MIDDLE  ALT=\"2pi\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "not even n=0, since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-pi ALIGN=MIDDLE  ALT=\"x+=+-pi\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "NOTE: x can't equal positive <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi ALIGN=MIDDLE  ALT=\"pi\"   DISABLED_style= \"max-width:90%; height:auto;\" > since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28pi%2F2%29+%3C%3E+-1 ALIGN=MIDDLE  ALT=\"sin%28pi%2F2%29+%3C%3E+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and the given equation: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28x%2F2%29-cos%28x%29=0 ALIGN=MIDDLE  ALT=\"sin%28x%2F2%29-cos%28x%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > would not be true!\r<BR>\n" );
document.write( "\n" );
document.write( "For <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2sin%28x%2F2%29-1+=+0 ALIGN=MIDDLE  ALT=\"2sin%28x%2F2%29-1+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2sin%28x%2F2%29+=+1 ALIGN=MIDDLE  ALT=\"2sin%28x%2F2%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28x%2F2%29+=+1%2F2 ALIGN=MIDDLE  ALT=\"sin%28x%2F2%29+=+1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Take the inverse Sin:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F2+=+pi%2F6%2B2n%2Api ALIGN=MIDDLE  ALT=\"x%2F2+=+pi%2F6%2B2n%2Api\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+pi%2F3%2B4n%2Api ALIGN=MIDDLE  ALT=\"x+=+pi%2F3%2B4n%2Api\"   DISABLED_style= \"max-width:90%; height:auto;\" >, n must = 0, else not within restriction, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+pi%2F3 ALIGN=MIDDLE  ALT=\"x+=+pi%2F3\"   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=x%2F2+=+5pi%2F6%2B2n%2Api ALIGN=MIDDLE  ALT=\"x%2F2+=+5pi%2F6%2B2n%2Api\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+5pi%2F3%2B4n%2Api ALIGN=MIDDLE  ALT=\"x+=+5pi%2F3%2B4n%2Api\"   DISABLED_style= \"max-width:90%; height:auto;\" >, n must = 0, else not within restriction, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+5pi%2F3 ALIGN=MIDDLE  ALT=\"x+=+5pi%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "So all values of x within restriction 0 to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2pi ALIGN=MIDDLE  ALT=\"2pi\"   DISABLED_style= \"max-width:90%; height:auto;\" > 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=5pi%2F3 ALIGN=MIDDLE  ALT=\"5pi%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >) </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );