document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=970967>Question 970967</A>: <I><SPAN STYLE=\"word-break: break-all;\"> i got 2n(pi) +or- pi/3 and 2n(pi) +or- pi as solutions for the equation cos x+cos 2x=0. but the book's answer says (2n+1)pi/3. I would like to know how could that be. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #593597 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39618)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=593597\">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%282x%29%2Bcos%28x%29-1=0 ALIGN=MIDDLE  ALT=\"cos%282x%29%2Bcos%28x%29-1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28x%29=-1 ALIGN=MIDDLE  ALT=\"cos%28x%29=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >  or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28x%29=1%2F2 ALIGN=MIDDLE  ALT=\"cos%28x%29=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Notice where x points to on the unit circle for these cosines.<BR>\n" );
document.write( "pi/3, 3pi/3, 5pi/3, and then as you continue to rotate in increments of to maintain those, you see difference of 2pi/3 each time.<BR>\n" );
document.write( "... next value for x would be  7pi/3.\r<BR>\n" );
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document.write( "...as you keep on thinking on this, notice that x will be ODD increments of pi/3.  Now observe that your numerator for x IS AN ODD NUMBER. </SPAN>\n" );
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