document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=590596>Question 590596</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do I find the polar coordinates of these rectangular points..(Sorry about the wording I'm so confused)?<BR>\n" );
document.write( "1. (-&#8730;3,-1)<BR>\n" );
document.write( "2. (-1,-&#8730;3)\r<BR>\n" );
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document.write( "I attempted two easier problems so if you could check them I'd appreciate it:)\r<BR>\n" );
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document.write( "1.(5,0)--> (5,&#960;)<BR>\n" );
document.write( "2.(0,-6)--> (&#960;,6) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #375218 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=375218\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "You want to convert from <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE (x,\,y)\"> to <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE (r,\,\theta)\">\r<BR>\n" );
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document.write( "Use the following relationships:\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\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \theta\ =\ \tan^{-1}\left(\Large{\frac{y}{x}}\LARGE\right)\">\r<BR>\n" );
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document.write( "For\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ (-\sqrt{3},\,-1)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ r^2\ =\ \left(-\sqrt{3}\right)^2\ +\ \left(-1\right)^2\ =\ 3\ +\ 1\ =\ 4\ \Rightarrow\ r\ =\ 2\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \theta\ =\ \tan^{-1}\left(\Large{\frac{-1}{-\sqrt{3}}}\LARGE\right)\">\r<BR>\n" );
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document.write( "So\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \tan\theta\ =\ \Large{\frac{-1}{-\sqrt{3}}\">\r<BR>\n" );
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document.write( "but tangent is the ratio of sine to cosine, so:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{\sin\theta}{\cos\theta}\ =\ \Large{\frac{-1}{-\sqrt{3}}\">\r<BR>\n" );
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document.write( "by the way, before we get too far along, notice that both <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE y\"> are negative which tells us that our point is in the third quadrant meaning that, whatever <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \theta\"> turns out to be, we are certain that it is in the interval <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \pi\ <\ \theta\ <\ \Large\frac{3\pi}{2}\">\r<BR>\n" );
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document.write( "Square both sides of:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{\sin\theta}{\cos\theta}\ =\ \Large{\frac{-1}{-\sqrt{3}}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{\sin^2\theta}{\cos^2\theta}\ =\ \Large{\frac{1}{3}\">\r<BR>\n" );
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document.write( "Then cross multiply:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \cos^2\theta\ =\ 3\left(\sin^2\theta\right)\">\r<BR>\n" );
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document.write( "A little algebra music, Sammy:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \cos^2\theta\ -\ 3\left(\sin^2\theta\right)\ =\ 0\">\r<BR>\n" );
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document.write( "Apply the Pythagorean Identity:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \cos^2\theta\ -\ 3\left(1\ -\ \cos^2\theta\right)\ =\ 0\">\r<BR>\n" );
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document.write( "Another chorus, Sammy:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 4\cos^2\theta\ -\ 3\ =\ 0\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \cos^2\theta\ =\ \frac{3}{4}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \cos\theta\ =\ \pm\frac{\sqrt{3}}{2}\">\r<BR>\n" );
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document.write( "Use the unit circle:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src=\"http://www.math.ucsd.edu/~jarmel/math4c/Unit_Circle_Angles.png\">\r<BR>\n" );
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document.write( "To see that the 3rd quadrant angle where <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \cos\theta\ =\ -\frac{\sqrt{3}}{2}\">\r<BR>\n" );
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document.write( "is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{4\pi}{3}\">\r<BR>\n" );
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document.write( "So the polar coordinate point is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(2, \frac{4\pi}{3}\right)\">\r<BR>\n" );
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document.write( "Do the other ones the same way, including the two that you did that are, in sum, 75% wrong.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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