document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=468905>Question 468905</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Convert the polar equation to rectangular form:\r<BR>\n" );
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document.write( "r=-2sin(theta)\r<BR>\n" );
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document.write( "Thanks!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #321832 by </B><A HREF=/tutors/aboutme.mpl?userid=ccs2011><B>ccs2011(207)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ccs2011><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=ccs2011><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=321832\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Use the following relationships:<BR>\n" );
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;\" ><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;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+sqrt%28x%5E2+%2B+y%5E2%29 ALIGN=MIDDLE  ALT=\"r+=+sqrt%28x%5E2+%2B+y%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now substitute into given equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+-2%2Asin%28theta%29 ALIGN=MIDDLE  ALT=\"r+=+-2%2Asin%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Notice we can solve for sin(theta)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28theta%29+=+y%2Fr+=+y%2Fsqrt%28x%5E2+%2B+y%5E2%29 ALIGN=MIDDLE  ALT=\"sin%28theta%29+=+y%2Fr+=+y%2Fsqrt%28x%5E2+%2B+y%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Thus equation becomes<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%5E2+%2B+y%5E2%29+=+-2%2A%28y%2Fsqrt%28x%5E2+%2B+y%5E2%29%29 ALIGN=MIDDLE  ALT=\"sqrt%28x%5E2+%2B+y%5E2%29+=+-2%2A%28y%2Fsqrt%28x%5E2+%2B+y%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply by sqrt(x^2 + y^2) on both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+y%5E2+=+-2y ALIGN=MIDDLE  ALT=\"x%5E2+%2B+y%5E2+=+-2y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Add 2y to both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+y%5E2+%2B2y+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+y%5E2+%2B2y+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Use completing the square to obtain standard circle equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+y%5E2+%2B+2y+%2B1+=+1 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+y%5E2+%2B+2y+%2B1+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+%28y%2B1%29%5E2+=+1 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+%28y%2B1%29%5E2+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Therefore polar equation is converted to rectangular form and is the graph of a circle of radius 1 centered at (0,-1). </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );