document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=70001>Question 70001</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the rectangular coordinates of a particular point are x=7, y=-24, find the polar coordinates.. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #49854 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=49854\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the rectangular coordinates of a particular point are x=7, y=-24, find the polar coordinates...\r<BR>\n" );
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document.write( "Note that since the value of y is negative and the value of x is positive.  This puts<BR>\n" );
document.write( "the point in quadrant IV.\r<BR>\n" );
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document.write( "The magnitude of the radius of is the hypotenuse of a right triangle with legs of length <BR>\n" );
document.write( "7 and 24.  Use the Pythagorean theorem to find this hypotenuse (H).\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=H+=+sqrt%287%5E2+%2B+24%5E2%29 ALIGN=MIDDLE  ALT=\"H+=+sqrt%287%5E2+%2B+24%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=H+=+sqrt%2849%2B576%29+=+sqrt%28625%29+=+25 ALIGN=MIDDLE  ALT=\"H+=+sqrt%2849%2B576%29+=+sqrt%28625%29+=+25\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "That gives us Magnitude.  All we need now is the angle.  The ratio of the angle is legs<BR>\n" );
document.write( "of the triangle are: <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2Fx=%28-24%2F7%29=+-3.428571429 ALIGN=MIDDLE  ALT=\"y%2Fx=%28-24%2F7%29=+-3.428571429\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This meets the definition of the tangent of the angle whose opposite side is -24 and whose<BR>\n" );
document.write( "adjacent side is +7.  Notice how this falls into quadrant IV = Since this ratio is the <BR>\n" );
document.write( "tangent, by applying arctangent on a calculator, we find that the angle is -73.73979 degrees.  \r<BR>\n" );
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document.write( "The polar form can be written in two ways:\r<BR>\n" );
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document.write( "   25/-73.73979\r<BR>\n" );
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document.write( "which means a magnitude of 25 units with an angle found by rotating the magnitude<BR>\n" );
document.write( "clockwise from positive portion of the x-axis by the amount 73.73979 degrees.\r<BR>\n" );
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document.write( "The angle can also be established by rotating (360-73.73979 or 286.26021 degrees)<BR>\n" );
document.write( "counter-clockwise from the positive portion of the x-axis.  This would be written as:\r<BR>\n" );
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document.write( "    25/286.26021\r<BR>\n" );
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document.write( "I hope this helps you to understand the relationship between the Cartesian and polar representations<BR>\n" );
document.write( "of points and specifically how to change from rectangular to polar form.\r<BR>\n" );
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document.write( "You may also find it helpful to make a rough sketch of the rectangular point (7,-24) and<BR>\n" );
document.write( "draw the magnitude (radius) from the origin to this point.  Measure out 7 on the positive<BR>\n" );
document.write( "x-axis and the vertical distance from the point (7,0) to the point (7, -24).  This will<BR>\n" );
document.write( "help you to see the right triangle (0,0) to (7,0), from (7,0) to (7, -24), and then from<BR>\n" );
document.write( "(7, -24) to (0,0).  The two points (7, -24) to (0,0) are the ends of the radius and the<BR>\n" );
document.write( "Magnitude of this line can also be found using the formula for the distance between two points.<BR>\n" );
document.write( "the tangent of the angle is the ratio of the length of the line (7,0) to (7, -24) over <BR>\n" );
document.write( "the length of the line from (0,0) to (7,0). Such a rough sketch will help you to visualize<BR>\n" );
document.write( "the problem.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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