document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1126640>Question 1126640</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to three decimal places where appropriate. If there is no solution, enter NO SOLUTION.)<BR>\n" );
document.write( "(tan2(&#952;) &#8722; 16)(2 cos(&#952;) + 1) = 0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #743005 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13219)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=743005\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The product is 0 when either factor is 0.<br><BR>\n" );
document.write( "---------------------------------------<br><BR>\n" );
document.write( "skip these lines; I solved the wrong equation...<br><BR>\n" );
document.write( "The second factor is 0 when cos(2x) = -1; the solutions are<BR>\n" );
document.write( "2x = 2pi/3 +/- 2k(pi)  -->  x = pi/3 +/- k(pi)<BR>\n" );
document.write( " or<BR>\n" );
document.write( "2x = 4pi/3 +/- 2k(pi)  -->  x = 2pi/3 +/- k(pi)<br><BR>\n" );
document.write( "-------------------------------------------<br><BR>\n" );
document.write( "here is the corrected discussion of the second factor...<br><BR>\n" );
document.write( "The second factor is 0 when 2cos(x) = -1, or cos(x) = -1/2.  The solutions are<BR>\n" );
document.write( "2pi/3 +/- 2k(pi)<BR>\n" );
document.write( "or<BR>\n" );
document.write( "4pi/3 +/- 2k(pi)<br><BR>\n" );
document.write( "The first factor does not have exact zeros, the way the second one does.  Its zeros are when<BR>\n" );
document.write( "tan(2x) = 16<BR>\n" );
document.write( "2x = arctan(16) +/- k(pi)<BR>\n" );
document.write( "x = (1/2)arctan(16) +/-(k/2)(pi)<br><BR>\n" );
document.write( "Use a calculator to get those zeros to the prescribed accuracy. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );