document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=521115>Question 521115</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the equation on the interval 0 less than or equal to theta which is less than 2pi.<BR>\n" );
document.write( "cos(2theta) + 6sin2theta = 4\r<BR>\n" );
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document.write( "Thank you!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #346353 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=346353\">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( "I assume you mean:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \cos\left(2\theta\right)\ +\ 6\sin^2\left(\theta\right)\ =\ 4\">\r<BR>\n" );
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document.write( "(Note, use the caret mark (Shift-6: ^) to indicate raising to a power as in sin^2(theta))\r<BR>\n" );
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document.write( "Use the Double Angle formula for cosine:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \cos^2(\theta)\ -\ \sin^2(\theta)\ +\ 6\sin^2(\theta)\ =\ 4\">\r<BR>\n" );
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document.write( "Use the Pythagorean Identity to change the cosine term to a sine term:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 1\ -\ \sin^2(\theta)\ -\ \sin^2(\theta)\ +\ 6\sin^2(\theta)\ =\ 4\">\r<BR>\n" );
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document.write( "A little Algebra Music, Maestro:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 4\sin^2(\theta)\ =\ 3\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \sin(\theta)\ =\ \pm\frac{\sqrt{3}}{2}\">\r<BR>\n" );
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document.write( "You will find these two <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y\"> values four places on the unit circle in the interval <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 0\ <\ \theta\ <\ 2\pi\">\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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