document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1125838>Question 1125838</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Sin^4 2theta -2 sin^2 2theta = -1<BR>\n" );
document.write( "(3tan 3theta)^2-27=0<BR>\n" );
document.write( "Solve for theta. Solutions should have exact radian measures such that 0<theta<2pi.<BR>\n" );
document.write( "(< is equal to or greater than) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #742148 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</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=742148\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "First equation....<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%282x%29%5E4-2%2Asin%282x%29%5E2%2B1+=+0 ALIGN=MIDDLE  ALT=\"sin%282x%29%5E4-2%2Asin%282x%29%5E2%2B1+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sin%282x%29%5E2-1%29%5E2+=+0 ALIGN=MIDDLE  ALT=\"%28sin%282x%29%5E2-1%29%5E2+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%282x%29%5E2-1+=+0 ALIGN=MIDDLE  ALT=\"sin%282x%29%5E2-1+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sin%282x%29-1%29%28sin%282x%29%2B1%29+=+0 ALIGN=MIDDLE  ALT=\"%28sin%282x%29-1%29%28sin%282x%29%2B1%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%282x%29+=+1 ALIGN=MIDDLE  ALT=\"sin%282x%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >  or  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%282x%29+=+-1 ALIGN=MIDDLE  ALT=\"sin%282x%29+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "0 < x < 2pi  -->  0 < 2x < 4pi<br><BR>\n" );
document.write( "On (0,4pi), sin(x) is 1 or -1 at pi/2, 3pi/2, 5pi/2, and 7pi/2.<br><BR>\n" );
document.write( "On (0,2pi), sin(2x) is 1 or -1 at pi/2, 3pi/2, 5pi/2, and 7pi/2.<br><BR>\n" );
document.write( "So the solution set for this equation, for x on (0,2pi), is<br><BR>\n" );
document.write( "{pi/4, 3pi/4, 5pi/4, 7pi/4}<br><BR>\n" );
document.write( "Second equation....<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283tan%283x%29%29%5E2+=+27 ALIGN=MIDDLE  ALT=\"%283tan%283x%29%29%5E2+=+27\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%28tan%283x%29%29%5E2+=+27 ALIGN=MIDDLE  ALT=\"9%28tan%283x%29%29%5E2+=+27\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28tan%283x%29%29%5E2+=+3 ALIGN=MIDDLE  ALT=\"%28tan%283x%29%29%5E2+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%283x%29+=+sqrt%283%29 ALIGN=MIDDLE  ALT=\"tan%283x%29+=+sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%283x%29+=+-sqrt%283%29 ALIGN=MIDDLE  ALT=\"tan%283x%29+=+-sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "0 < x < 2pi  -->  0 < 3x < 6pi<br><BR>\n" );
document.write( "On (0,6pi), tan(x) is sqrt(3) or -sqrt(3) at pi/3, 2pi/3, 4pi/3, 5pi/3, 7pi/3, 8pi/3, 10pi/3, 11pi/3, 13pi/3, 14pi/3, 16pi/3, and 17pi/3.<br><BR>\n" );
document.write( "On (0,2pi), tan(3x) is sqrt(3) or -sqrt(3) at pi/9, 2pi/9, 4pi/9, 5pi/9, 7pi/9, 8pi/9, 10pi/9, 11pi/9, 13pi/9, 14pi/9, 16pi/9, and 17pi/9.<br><BR>\n" );
document.write( "So the solution set for this equation, for x on (0,2pi), is<br><BR>\n" );
document.write( "{pi/9, 2pi/9, 4pi/9, 5pi/9, 7pi/9, 8pi/9, 10pi/9, 11pi/9, 13pi/9, 14pi/9, 16pi/9, 17pi/9}<br> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );