document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=623700>Question 623700</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please if someone could kindly help me with this question. Thank you.\r<BR>\n" );
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document.write( "Solve for all possible x in (o, 360 degrees): 2 sin x = 2 cos 2x\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #392248 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=392248\">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( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 2\sin(x)\ =\ 2\cos(2x)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \sin(x)\ =\ \cos(2x)\">\r<BR>\n" );
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document.write( "Use\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \cos(2\varphi)\ =\ \cos^2(\varphi)\ -\ \sin^2(\varphi)\">\r<BR>\n" );
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document.write( "To write:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \sin(x)\ =\ \cos^2(x)\ -\ \sin^2(x)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \sin^2(x)\ +\ \sin(x)\ =\ \cos^2(x)\">\r<BR>\n" );
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document.write( "Use the Pythagorean Identity\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \cos^2(\varphi)\ +\ \sin^2(\varphi)\ =\ 1\">\r<BR>\n" );
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document.write( "to write:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \sin^2(x)\ +\ \sin(x)\ =\ 1\ -\ \sin^2(x)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 2\sin^2(x)\ +\ \sin(x)\ -\ 1\ =\ 0\">\r<BR>\n" );
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document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE u\ =\ \sin(x)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 2u^2\ +\ u\ -\ 1\ =\ 0\">\r<BR>\n" );
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document.write( "Solve the quadratic.  It factors, but clumsily; the quadratic equation will be faster.\r<BR>\n" );
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document.write( "Substitute back: <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sin(x)\ =\ u\">, giving you 2 values for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sin(x)\">.  Find the three angles in the given interval on the unit cirle that satisfy your two values for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sin(x)\">\r<BR>\n" );
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document.write( "Hint: <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sin(x)\"> is the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE y\">-coordinate.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src=\"http://www.math.ucsd.edu/~jarmel/math4c/Unit_Circle_Angles.png\">\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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