document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=631549>Question 631549</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use rapid sketching techniques to graph r = 3 - 6 cos theta. Be sure to show how you arrived at your graph. Only use calculator to check. Thanks!  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #397668 by </B><A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><B>Edwin McCravy(20060)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><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=Edwin+McCravy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=397668\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> r = 3 - 6 cos theta<BR>\n" );
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document.write( "r is a relative minimum when cos(@) is a relative maximum\r\n" );
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document.write( "cos@ is an absolute and a relative maximum of 1 when @ = 0,  \r\n" );
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document.write( "therefore r is a relative minimum when @ = 0, r = 3 - 6(1) = -3\r\n" );
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document.write( "So we plot the polar point (-3,0) [which is the rectangular point (-3,0)]\r\n" );
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document.write( "That is the end of the inner loop.\r\n" );
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document.write( "r is a relative maximum when cos(@) is a relative minimum\r\n" );
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document.write( "cos@ is an absolute and relative minimum of -1 when @ = pi, therefore \r\n" );
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document.write( "r is a relative maximum when @ = pi, r = 3 - 6(-1) = 9\r\n" );
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document.write( "So we plot (9,pi), [which is the rectangular point (-9,0)] \r\n" );
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document.write( "That is the end of the outer loop.\r\n" );
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document.write( "The y-intercepts are found when @ = pi/2 a,d 3pi/2\r\n" );
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document.write( "r = 3 - 6 cos(pi/2) \r\n" );
document.write( "r = 3 - 6·0\r\n" );
document.write( "r = 3    \r\n" );
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document.write( "So they are the polar point (3,pi/2) and (3,3pi/2)\r\n" );
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document.write( "which are the rectangular points (0,3) amd (0,-3)\r\n" );
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document.write( "The graph is like this:\r\n" );
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document.write( "Edwin</PRE> </SPAN>\n" );
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