document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1206408>Question 1206408</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me with this equation.<BR>\n" );
document.write( "An equation is given. (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( "1 − 2 sin(𝜃) = cos(2𝜃)<BR>\n" );
document.write( "Find the solutions in the interval [0, 2𝜋). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #843854 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=843854\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+-2+sin%28theta%29+=+cos%282theta%29 ALIGN=MIDDLE  ALT=\"1+-2+sin%28theta%29+=+cos%282theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Find the solutions in the interval [<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2pi ALIGN=MIDDLE  ALT=\"2pi\"   DISABLED_style= \"max-width:90%; height:auto;\" >).\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+-2+sin%28theta%29+=+cos%282theta%29 ALIGN=MIDDLE  ALT=\"1+-2+sin%28theta%29+=+cos%282theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >....use identity <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%282theta%29=cos%5E2%28theta%29+-+sin%5E2%28theta%29 ALIGN=MIDDLE  ALT=\"cos%282theta%29=cos%5E2%28theta%29+-+sin%5E2%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+-2+sin%28theta%29+=+cos%5E2%28theta%29+-+sin%5E2%28theta%29 ALIGN=MIDDLE  ALT=\"1+-2+sin%28theta%29+=+cos%5E2%28theta%29+-+sin%5E2%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%5E2%28theta%29-cos%5E2%28theta%29+-2+sin%28theta%29+%2B1=+0 ALIGN=MIDDLE  ALT=\"sin%5E2%28theta%29-cos%5E2%28theta%29+-2+sin%28theta%29+%2B1=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >...use identity <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%5E2%28theta%29=1-sin%5E2%28theta%29 ALIGN=MIDDLE  ALT=\"cos%5E2%28theta%29=1-sin%5E2%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%5E2%28theta%29-%281-sin%5E2%28theta%29%29+-2+sin%28theta%29+%2B1=+0 ALIGN=MIDDLE  ALT=\"sin%5E2%28theta%29-%281-sin%5E2%28theta%29%29+-2+sin%28theta%29+%2B1=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%5E2%28theta%29-1%2Bsin%5E2%28theta%29+-2+sin%28theta%29+%2B1=+0 ALIGN=MIDDLE  ALT=\"sin%5E2%28theta%29-1%2Bsin%5E2%28theta%29+-2+sin%28theta%29+%2B1=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2sin%5E2%28theta%29+-2+sin%28theta%29+=+0 ALIGN=MIDDLE  ALT=\"2sin%5E2%28theta%29+-2+sin%28theta%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >...factor\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2sin%28theta%29%28sin%28theta%29+-1%29++=+0 ALIGN=MIDDLE  ALT=\"2sin%28theta%29%28sin%28theta%29+-1%29++=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "solutions:\r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2sin%28theta%29+=+0 ALIGN=MIDDLE  ALT=\"2sin%28theta%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > =><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28theta%29+=+0 ALIGN=MIDDLE  ALT=\"sin%28theta%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2sin%28theta%29-1+=+0 ALIGN=MIDDLE  ALT=\"2sin%28theta%29-1+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > =><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28theta%29+=+1%2F2 ALIGN=MIDDLE  ALT=\"sin%28theta%29+=+1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta ALIGN=MIDDLE  ALT=\"theta\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta=sin%5E-1%280%29 ALIGN=MIDDLE  ALT=\"theta=sin%5E-1%280%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta=0 ALIGN=MIDDLE  ALT=\"theta=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (result in radians) or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta=0 ALIGN=MIDDLE  ALT=\"theta=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >°<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta=sin%5E-1%281%2F2%29 ALIGN=MIDDLE  ALT=\"theta=sin%5E-1%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta=+pi%2F6 ALIGN=MIDDLE  ALT=\"theta=+pi%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > (result in radians) or<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta=30 ALIGN=MIDDLE  ALT=\"theta=30\"   DISABLED_style= \"max-width:90%; height:auto;\" >°\r<BR>\n" );
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document.write( "the solutions in the interval [<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2pi ALIGN=MIDDLE  ALT=\"2pi\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta=0 ALIGN=MIDDLE  ALT=\"theta=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta=0 ALIGN=MIDDLE  ALT=\"theta=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >°<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta=pi%2F6 ALIGN=MIDDLE  ALT=\"theta=pi%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > or<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta=30 ALIGN=MIDDLE  ALT=\"theta=30\"   DISABLED_style= \"max-width:90%; height:auto;\" >°<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta=5pi%2F6 ALIGN=MIDDLE  ALT=\"theta=5pi%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > or<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta=150 ALIGN=MIDDLE  ALT=\"theta=150\"   DISABLED_style= \"max-width:90%; height:auto;\" >°<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta=pi ALIGN=MIDDLE  ALT=\"theta=pi\"   DISABLED_style= \"max-width:90%; height:auto;\" > or<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta=180 ALIGN=MIDDLE  ALT=\"theta=180\"   DISABLED_style= \"max-width:90%; height:auto;\" >°\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );