document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1086221>Question 1086221</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Help please:\r<BR>\n" );
document.write( "\n" );
document.write( "2sin^2(theta) - cos(theta) - 1 = 0, on [0,2pi]\r<BR>\n" );
document.write( "\n" );
document.write( "Thank you.   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #700391 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=700391\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> For simplicity, we let x = theta.<BR>\n" );
document.write( "To get an equation in cos(x), use the identity sin^2(x) = 1-cos^2(x)<BR>\n" );
document.write( "Then we have<BR>\n" );
document.write( "2(1 - cos^2(x)) - cos(x) - 1 = 0<BR>\n" );
document.write( "2cos^2(x) + cos(x) - 1 = 0<BR>\n" );
document.write( "Factor:<BR>\n" );
document.write( "(2cos(x) - 1)(cos(x) + 1) = 0<BR>\n" );
document.write( "This has two solutions, cos(x) = -1 and cos(x) = 1/2<BR>\n" );
document.write( "I leave it as an exercise to determine the values of x which satisfy the two conditions. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );