document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1193294>Question 1193294</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine the solutions to sin^2 θ = -sin θ where -π≤x<π </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #825325 by </B><A HREF=/tutors/aboutme.mpl?userid=Solver92311><B>Solver92311(821)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Solver92311><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=Solver92311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=825325\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \theta\"> are two entirely different things, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large -\pi\,\leq\,x\,<\,\pi\"> is meaningless with respect to the given equation.  Therefore you must need the solution for all real values of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \theta\">\r<BR>\n" );
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document.write( "[1]<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \sin^2(\theta)\ =\ -\sin(\theta)\">\r<BR>\n" );
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document.write( "[2]<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \sin(\theta)\,\cdot\,\sin(\theta)\ =\ -\sin(\theta)\">\r<BR>\n" );
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document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \sin(\theta)\ =\ 0\ \Leftrightarrow\ \theta\ =\ k\pi\ |\ k\ \in\ \mathbb{Z}\">,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \theta\ =\ k\pi\ |\ k\ \in\ \mathbb{Z}\"> is a partial solution.\r<BR>\n" );
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document.write( "Furthermore, dividing eq. [2] by <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \sin(\theta)\"> gives \r<BR>\n" );
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document.write( "[3]<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \sin(\theta)\ =\ -1\">\r<BR>\n" );
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document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \sin(\theta)\ =\ -1\ \Leftrightarrow\ \theta\ =\ \frac{3\pi}{2}\ +\ k\pi\ |\ k\ \in\ \mathbb{Z}\">,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{3\pi}{2}\ +\ k\pi\ |\ k\ \in\ \mathbb{Z}\"> is also part of the solution set.\r<BR>\n" );
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document.write( "In sum, the solution set is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \{k\pi,\,\frac{3\pi}{2}\,+\,k\pi\ |\ k\ \in\ \mathbb{Z}\ }\">\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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document.write( "From <https://www.algebra.com/cgi-bin/upload-illustration.mpl> <BR>\n" );
document.write( "I > Ø<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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