document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=78336>Question 78336</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find all solutions to the equation on the interval [0,2pie)  cos(2theta)-tan(theta)=1<BR>\n" );
document.write( "Here is my work:  *=theta<BR>\n" );
document.write( "cos(2*)-tan(*)-1=0<BR>\n" );
document.write( "1-2sin^2(*)-sin(*)/cos(*)-1=0<BR>\n" );
document.write( "cos(*)-2sin^2(*)cos(*)-sin(*)-cos(*)=0<BR>\n" );
document.write( "-2sin^2(*)cos(*)-sin(*)=0<BR>\n" );
document.write( "-Sin(*)[2sin(*)cos(*)-1]=0<BR>\n" );
document.write( "-sin(*)=0               2sin(*)cos(*)=0<BR>\n" );
document.write( "-(*)=-pie/2,-3pie/2     sin(*)=0               cos(*)=0<BR>\n" );
document.write( "                        (*)=pie/2,3pie/2       (*)=pie, 2pie<BR>\n" );
document.write( "Did I do this correctly? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #56171 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=56171\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You're right so far, but lets look at this step \"-2sin^2(*)cos(*)-sin(*)=0\"\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large sin(\theta)[-2sin(\theta)cos(\theta)-1]=0\"> Factor out a <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large sin(\theta)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large sin(\theta)=0\"> Set the first term equal to zero\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large \theta=0+n\pi\"> Take the arcsine of both sides\r<BR>\n" );
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document.write( "So for this solution you should have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large \theta=0\"> (if we let n=0), <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large \theta=\pi\"> (if we let n=1)\r<BR>\n" );
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document.write( "Now let  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large -2sin(\theta)cos(\theta)-1\"> equal zero<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large -2sin(\theta)cos(\theta)-1=0\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large -sin(2\theta)-1=0\"> Replace <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large 2sin(\theta)cos(\theta)\"> with <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large sin(2\theta)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large -sin(2\theta)=1\"> Add 1 to both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large -2\theta=\frac{\pi}{2}+n\pi\"> Take the arc sine of both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large \theta=\frac{-\pi}{4}+n\pi\"> Divide both sides by -2\r<BR>\n" );
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document.write( "So just looking in the interval [0,<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large 2\pi\">) (excluding <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large 2\pi\">) we get the solutions \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large \theta=\frac{-\pi}{4}+\pi=\frac{3\pi}{4}\"> Let n=1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large \theta=\frac{-\pi}{4}+2\pi=\frac{7\pi}{4}\"> Let n=2\r<BR>\n" );
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document.write( "So we only have 4 solutions in the interval [0,<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large 2\pi\">):\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large \theta=0\">, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large \theta=\frac{3\pi}{4}\">, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large \theta=\pi\">, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large \theta=\frac{7\pi}{4}\"> </SPAN>\n" );
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