document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=122525>Question 122525</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 11)    A rectangular equation equivalent to r = sin(theta) is:\r<BR>\n" );
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document.write( "a)       x^2 + y^2 = y\r<BR>\n" );
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document.write( "b)       x^2 + y^2 = x\r<BR>\n" );
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document.write( "c)       x^2 – y^2 = y\r<BR>\n" );
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document.write( "d)       x^2 – y^2 = x\r<BR>\n" );
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document.write( "e)       none of these\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #89937 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=89937\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> # 11<BR>\n" );
document.write( "Using the conversion formulas that convert polar to rectangular, we have \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE y=r\sin(\theta)\"> (since we're dealing with sine) and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE r=\sqrt{x^{2}+y^{2}}\"> \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE r^{2}=x^{2}+y^{2}\"> Now square both sides of the second formula\r<BR>\n" );
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document.write( " ------------------ Now let's manipulate <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE r=\sin(\theta)\">: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE r^2=r\sin(\theta)\"> Multiply both sides by r \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x^{2}+y^{2}=r\sin(\theta)\"> Replace <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE r^{2}\"> with <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x^{2}+y^{2}\">. Remember, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE r^{2}=x^{2}+y^{2}\"> \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x^{2}+y^{2}=y\"> Replace <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE r\sin(\theta)\"> with <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE y\">. Remember, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE y=r\sin(\theta)\"> \r<BR>\n" );
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document.write( "So the polar equation <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE r=\sin(\theta)\"> converts to <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x^{2}+y^{2}=y\"> So the answer is A) <BR>\n" );
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