document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=381159>Question 381159</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What are the possible values of x domain: [0,2pi). \r<BR>\n" );
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document.write( "4sin^3(x) + 2sin^2(x) = 2sin(x) + 1\r<BR>\n" );
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document.write( "So far I've:\r<BR>\n" );
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document.write( "set equal to zero: <BR>\n" );
document.write( "4sin^3(x) + 2sin^2(x) + 2sin(x) + 1 = 0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #270515 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=270515\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First of all when you set everything equal to zero you should obtain\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4+sin%5E3+%28x%29+%2B+2+sin%5E2+%28x%29+-+2+sin+x+-+1+=+0 ALIGN=MIDDLE  ALT=\"4+sin%5E3+%28x%29+%2B+2+sin%5E2+%28x%29+-+2+sin+x+-+1+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Let a = sin x. The equation then becomes\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4a%5E3+%2B+2a%5E2+-+2a+-+1+=+0 ALIGN=MIDDLE  ALT=\"4a%5E3+%2B+2a%5E2+-+2a+-+1+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This is equivalent to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4a%5E3+-+2a+%2B+2a%5E2+-+1+=+0 ALIGN=MIDDLE  ALT=\"4a%5E3+-+2a+%2B+2a%5E2+-+1+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >. We can factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2a%5E2+-1 ALIGN=MIDDLE  ALT=\"2a%5E2+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > to obtain\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282a%5E2+-+1%29%282a+%2B+1%29+=+0 ALIGN=MIDDLE  ALT=\"%282a%5E2+-+1%29%282a+%2B+1%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Solving, we obtain a = -1/2, sqrt(2)/2, and -sqrt(2)/2. All of these values are between -1 and 1, so we can find sin^-1 of each of these angles to find all values for x:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%5E%28-1%29+%28-1%2F2%29+=+%287pi%2F6%29 ALIGN=MIDDLE  ALT=\"sin%5E%28-1%29+%28-1%2F2%29+=+%287pi%2F6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2811pi%2F6%29 ALIGN=MIDDLE  ALT=\"%2811pi%2F6%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%5E%28-1%29+%28sqrt%282%29%2F2%29+=+pi%2F4 ALIGN=MIDDLE  ALT=\"sin%5E%28-1%29+%28sqrt%282%29%2F2%29+=+pi%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3pi%2F4 ALIGN=MIDDLE  ALT=\"3pi%2F4\"   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%5E%28-1%29+%28-sqrt%282%29%2F2%29+=+5pi%2F4 ALIGN=MIDDLE  ALT=\"sin%5E%28-1%29+%28-sqrt%282%29%2F2%29+=+5pi%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7pi%2F4 ALIGN=MIDDLE  ALT=\"7pi%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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