document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=998054>Question 998054</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do I eliminate theta from these two equations?\r<BR>\n" );
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document.write( "x = 3cos(2theta) + 1\r<BR>\n" );
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document.write( "y = 2sin(theta) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #615956 by </B><A HREF=/tutors/aboutme.mpl?userid=fractalier><B>fractalier(6550)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=fractalier><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=fractalier><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=615956\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given (let's call theta q)\r<BR>\n" );
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document.write( "x = 3cos(2q) + 1\r<BR>\n" );
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document.write( "y = 2sin(q)\r<BR>\n" );
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document.write( "the plan is to substitute the identity for cos(2q) that involves only sines... that is 1 - 2sin^2(q)...so that<BR>\n" );
document.write( "x = 3(1 - 2sin^2(q)) + 1<BR>\n" );
document.write( "We can get a value for sin(q) from the second equation...<BR>\n" );
document.write( "sin(q) = y/2<BR>\n" );
document.write( "Now plug that in and get<BR>\n" );
document.write( "x = 3(1 - 2(y/2)^2) + 1<BR>\n" );
document.write( "x = 3 - 6(y^2/4) + 1<BR>\n" );
document.write( "x = 4 - 3y^2/2<BR>\n" );
document.write( "It's a parabola. </SPAN>\n" );
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