document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1191359>Question 1191359</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Transform the following equation to a cartesian equation: r=sec(theta)tan^2(theta) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #823183 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=823183\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "Transform the following equation to a cartesian equation: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=sec%28theta%29%2Atan%5E2%28theta%29 ALIGN=MIDDLE  ALT=\"r=sec%28theta%29%2Atan%5E2%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "First convert the expression into terms of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28theta%29+ ALIGN=MIDDLE  ALT=\"cos%28theta%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28theta%29 ALIGN=MIDDLE  ALT=\"sin%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >...............<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sec%28theta%29=1%2Fcos%28theta%29+ ALIGN=MIDDLE  ALT=\"sec%28theta%29=1%2Fcos%28theta%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%5E2%28theta%29=sin%5E2%28theta%29%2Fcos%5E2%28theta%29 ALIGN=MIDDLE  ALT=\"tan%5E2%28theta%29=sin%5E2%28theta%29%2Fcos%5E2%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=%281%2Fcos%28theta%29+%29%28sin%5E2%28theta%29%2Fcos%5E2%28theta%29%29 ALIGN=MIDDLE  ALT=\"r=%281%2Fcos%28theta%29+%29%28sin%5E2%28theta%29%2Fcos%5E2%28theta%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=sin%5E2%28theta%29%2Fcos%5E3%28theta%29 ALIGN=MIDDLE  ALT=\"r=sin%5E2%28theta%29%2Fcos%5E3%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%2Acos%5E3%28theta%29=sin%5E2%28theta%29 ALIGN=MIDDLE  ALT=\"r%2Acos%5E3%28theta%29=sin%5E2%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now the normal substitutions are: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=r%2Acos%28theta%29 ALIGN=MIDDLE  ALT=\"x=r%2Acos%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  =><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28theta%29=x%2Fr ALIGN=MIDDLE  ALT=\"cos%28theta%29=x%2Fr\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=r%2Asin%28theta%29 ALIGN=MIDDLE  ALT=\"y=r%2Asin%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > =><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28theta%29=y%2Fr ALIGN=MIDDLE  ALT=\"sin%28theta%29=y%2Fr\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Substituting these values into the expression above gives\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%2A%28x%2Fr%29%5E3=%28y%2Fr%29%5E2 ALIGN=MIDDLE  ALT=\"r%2A%28x%2Fr%29%5E3=%28y%2Fr%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%2A%28x%5E3%2Fr%5E3%29=y%5E2%2Fr%5E2 ALIGN=MIDDLE  ALT=\"r%2A%28x%5E3%2Fr%5E3%29=y%5E2%2Fr%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3%2Fr%5E2=y%5E2%2Fr%5E2 ALIGN=MIDDLE  ALT=\"x%5E3%2Fr%5E2=y%5E2%2Fr%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3=y%5E2 ALIGN=MIDDLE  ALT=\"x%5E3=y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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