document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=687763>Question 687763</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this equation. <BR>\n" );
document.write( "find all solution [0,2pi)<BR>\n" );
document.write( "4sin(2x)+4cos(x)=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #425338 by </B><A HREF=/tutors/aboutme.mpl?userid=fcabanski><B>fcabanski(1391)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=fcabanski><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=425338\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Remember the double angle identity: sin(2a) = 2*sin(a)*cos(a).   <P><BR>\n" );
document.write( "4sin(2x)+4cos(x)=0 --->divide out the like term (4) ---> 4(sin(2x)+cos(x)) = 0 ---> (divide both sides by 4)---> sin(2x) + cos(x) = 0 (use the double angle identity.<P><BR>\n" );
document.write( "2sin(x)cos(x) + cos(x) = 0 ---> factor out like terms (cos(x) ---> cos(x)(2sin(x)+1) = 0  Now use the zero product rule.<P><BR>\n" );
document.write( "cos(x) = 0 which for the stated range is 90 degrees or pi/2.<P><BR>\n" );
document.write( "2sin(x) + 1 = 0 ---> 2sin(x) = -1 ---> sin(x) = -1/2 which is 210 degrees or 7pi/6 in the stated range.<BR>\n" );
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