document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=600086>Question 600086</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the solutions of the equation that are in the interval [0, 2&#960;). (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.)\r<BR>\n" );
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document.write( "cos u &#8722; cos 2u = 0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #379189 by </B><A HREF=/tutors/aboutme.mpl?userid=htmentor><B>htmentor(1343)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=htmentor><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=htmentor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=379189\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Since cos(2u) = 2*cos^2(u) - 1, we can write the equation as<BR>\n" );
document.write( "cos(u) - (2*cos^2(u) - 1) = 0<BR>\n" );
document.write( "2*cos^2(u) - cos(u) - 1 = 0<BR>\n" );
document.write( "Factor:<BR>\n" );
document.write( "(2*cos(u)+1)(cos(u)-1) = 0<BR>\n" );
document.write( "This gives cos(u) = -1/2 and cos(u) = 1<BR>\n" );
document.write( "On the interval 0 <= u < 2<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi ALIGN=MIDDLE  ALT=\"pi\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the solutions are u = 0, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Api%2F3 ALIGN=MIDDLE  ALT=\"2%2Api%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Api%2F3 ALIGN=MIDDLE  ALT=\"4%2Api%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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