document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=278377>Question 278377</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Give the polar coordinates: (-2, 2). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #202591 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=202591\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your cartesian coordinates are (-2,2)\r<BR>\n" );
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document.write( "x = -2<BR>\n" );
document.write( "y = 2\r<BR>\n" );
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document.write( "you want to convert from the form (x,y) to the form (r,T) where r is the length of the line segment and T is the angle.\r<BR>\n" );
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document.write( "T can be expressed in degrees or radians.\r<BR>\n" );
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document.write( "Some formulas to help you.\r<BR>\n" );
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document.write( "r = sqrt(x^2 + y^2)\r<BR>\n" );
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document.write( "T = arcTan (y/x)\r<BR>\n" );
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document.write( "In your problem, r = sqrt(4 + 4) = sqrt(8) = 2.828427125\r<BR>\n" );
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document.write( "T = arcTan (2/-2) = arcTan (-1) = -45 degrees.\r<BR>\n" );
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document.write( "If you add 180 to it, then it can also be 135 degrees.\r<BR>\n" );
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document.write( "Since in the cartesian coordinate system, your point is in the second quadrant, then in the polar coordinate system it also has to be in the second quadrant.\r<BR>\n" );
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document.write( "-45 degrees is in the fourth quadrant.\r<BR>\n" );
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document.write( "180 - 45 = 135 degrees is in the second quadrant.\r<BR>\n" );
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document.write( "135 degrees is the angle that you want, so T = 135 degrees.\r<BR>\n" );
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document.write( "your point of (-2,2) in the cartesian coordinate system is equivalent to the point (2.828427125, 135) in the polar coordinate system.\r<BR>\n" );
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document.write( "Your polar coordinates are (2.828427125,135) where T is expressed in degrees.\r<BR>\n" );
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document.write( "A calculator that can help you convert between polar and cartesian coordinate system can be found in the following reference.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"http://www.random-science-tools.com/maths/coordinate-converter.htm\" target = \"_blank\">http://www.random-science-tools.com/maths/coordinate-converter.htm</a> </SPAN>\n" );
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