document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=772232>Question 772232</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find all the solutions to the equations in the interval (0, 2pi.<BR>\n" );
document.write( "1. 2sin^2x=2+cosx<BR>\n" );
document.write( "2. 2sin^2x+3sinx+1=0<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #470784 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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=470784\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find all the solutions to the equations in the interval (0, 2pi.<BR>\n" );
document.write( "***<BR>\n" );
document.write( "1. 2sin^2x=2+cosx<BR>\n" );
document.write( "2(1-cos^2x)=2+cosx<BR>\n" );
document.write( "2-2cos^2x=2+cosx<BR>\n" );
document.write( "2cos^2x+cosx=0<BR>\n" );
document.write( "cosx(2cosx+1)=0<BR>\n" );
document.write( "..<BR>\n" );
document.write( "cosx=0<BR>\n" );
document.write( "no solution: (0 not in given domain)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "2cosx+1=0<BR>\n" );
document.write( "cosx=-1/2<BR>\n" );
document.write( "x=2pi/3, 5pi/3<BR>\n" );
document.write( "..<BR>\n" );
document.write( "2. 2sin^2x+3sinx+1=0<BR>\n" );
document.write( "solve for sinx using quadratic formula<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a=2, b=3, c=1<BR>\n" );
document.write( "ans:<BR>\n" );
document.write( "sinx=-1<BR>\n" );
document.write( "x=3pi/2<BR>\n" );
document.write( "or<BR>\n" );
document.write( "sinx=-1/2<BR>\n" );
document.write( "x=7pi/6, 11pi/6\r<BR>\n" );
document.write( "\n" );
document.write( "solutions:x=2pi/3, 5pi/3, 3pi/2, 7pi/6, 11pi/6 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );