c6a9cd69c2
* NEW: Add examples again. I hope correctly this time. git-svn-id: svn://localhost/gambas/trunk@6726 867c0c6c-44f3-4631-809d-bfa615b0a4ec
150 lines
5.6 KiB
HTML
150 lines
5.6 KiB
HTML
<!DOCTYPE html PUBLIC "-//w3c//dtd html 3.2//en">
|
|
<html>
|
|
<head>
|
|
<title>Polar Coordinates</title>
|
|
<meta name="author" content="Michael Isaac">
|
|
</head>
|
|
<body alink="#ffff00" background="" bgcolor="#ffffff" link="#0000ff"
|
|
text="#000000" vlink="#ff0000">
|
|
<center>
|
|
<table style="width: 730px; height: 600px;">
|
|
<tbody>
|
|
<tr>
|
|
<td align="left"> <font face="arial, times new roman" size="2">
|
|
<center><font
|
|
style="font-weight: bold; font-family: helvetica,arial,sans-serif;"
|
|
size="+3">Polar
|
|
Coordinates</font><br style="font-family: helvetica,arial,sans-serif;">
|
|
<font style="font-family: helvetica,arial,sans-serif;" size="-1">converting
|
|
(r, d) to (x, y)</font><br>
|
|
</center>
|
|
<br>
|
|
<center>
|
|
<table width="500">
|
|
<tbody>
|
|
<tr>
|
|
<td align="left"> <font face="arial" size="2"> <img
|
|
src=".html_files/eg3.gif" alt="" align="left" height="137" hspace="20"
|
|
width="119"><br>
|
|
</font>
|
|
<div style="text-align: left;"><font
|
|
style="font-family: helvetica,arial,sans-serif;" size="-1">Here's a
|
|
point shown using polar
|
|
coordinates. </font><br>
|
|
<font style="font-family: helvetica,arial,sans-serif;"
|
|
size="-1">It would be labeled <span style="font-weight: bold;">(r</span><span
|
|
style="font-weight: bold;">,</span> <span style="font-weight: bold;">d</span><b>)
|
|
</b>or<b> (4, 300°)</b> for this point.<b><br>
|
|
</b></font><font style="font-family: monospace;" size="+1"></font><br>
|
|
<font face="arial" size="2"> </font></div>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table>
|
|
</center>
|
|
<br>
|
|
</font><font face="arial, times new roman" size="2"> </font><font
|
|
face="arial, times new roman" size="2">
|
|
<center>
|
|
<div style="text-align: justify;"> </div>
|
|
<table width="720">
|
|
<tbody>
|
|
<tr>
|
|
<td align="left" valign="top" width="480">
|
|
<div style="text-align: justify;">
|
|
<div style="text-align: justify;"> <font
|
|
style="font-family: helvetica,arial,sans-serif;" size="-1">The
|
|
point <span style="font-weight: bold;">(x, y)</span>
|
|
can be located by finding the horizontal and vertical components
|
|
of <span style="font-weight: bold;">r</span>. We can do that by
|
|
substituting the radius and the degree<span style="font-weight: bold;"></span>
|
|
<span style="font-weight: bold;">(r, d)</span> into the
|
|
following formulas.<br>
|
|
</font></div>
|
|
</div>
|
|
<font face="arial" size="2"><br>
|
|
</font>
|
|
<div style="text-align: center;"><font
|
|
face="arial, times new roman"><font face="arial, times new roman"><font
|
|
face="arial, times new roman"><font style="font-family: monospace;">x
|
|
= r * cos(d)</font></font></font></font><br
|
|
style="font-family: monospace;">
|
|
<font face="arial, times new roman"><font
|
|
face="arial, times new roman"><font face="arial, times new roman"> <font
|
|
style="font-family: monospace;">y = r *
|
|
sin(d)<br>
|
|
<br>
|
|
</font></font></font></font>
|
|
<div style="text-align: left;"><font size="-1"><span
|
|
style="font-family: helvetica,arial,sans-serif;">So we end up with;</span></font><br>
|
|
<br>
|
|
</div>
|
|
</div>
|
|
<div style="text-align: center; font-family: monospace;">x
|
|
= 4 * cos(300) = 2<br>
|
|
y = 4 * sin(300) = -3.46 </div>
|
|
<font style="font-family: monospace;"> </font><br>
|
|
<br>
|
|
<div style="text-align: justify;"><font
|
|
style="font-family: helvetica,arial,sans-serif;" size="-1">As we can
|
|
see, the
|
|
point <b>(4, 300°)</b>
|
|
in
|
|
polar coordinates is equivalent to a point with the rectangular
|
|
coordinates <b>(2, -3.46)<br>
|
|
</b></font><font
|
|
style="font-family: helvetica,arial,sans-serif;" size="-1"></font><font
|
|
face="arial" size="2"> </font></div>
|
|
</td>
|
|
<td align="right" valign="top" width="240"> <font
|
|
face="arial" size="2"><img src=".html_files/eg3b.gif" alt=""
|
|
height="222" width="223"> <br>
|
|
</font>
|
|
<div style="text-align: center;"><font
|
|
face="arial, times new roman" size="2"><font
|
|
face="arial, times new roman" size="2"><font
|
|
style="font-family: monospace;" size="+1"><br>
|
|
x = r * cos(d)</font></font></font><br style="font-family: monospace;">
|
|
<font face="arial, times new roman" size="2"><font
|
|
face="arial, times new roman" size="2"><font size="+1"> </font> <font
|
|
style="font-family: monospace;" size="+1">y = r *
|
|
sin(d)</font></font></font><br>
|
|
</div>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table>
|
|
</center>
|
|
</font>
|
|
<center>
|
|
<table
|
|
style="text-align: left; margin-left: auto; margin-right: auto; width: 275px; height: 68px;">
|
|
<tbody>
|
|
<tr>
|
|
<td style="text-align: center;"><font
|
|
style="font-family: helvetica,arial,sans-serif;" size="-2">Content by <a
|
|
href="mailto:subjugator@gmail.com">Michael Isaac</a>, 2004<br>
|
|
</font><font
|
|
style="font-family: helvetica,arial,sans-serif;" size="-2">Original </font><font
|
|
style="font-family: helvetica,arial,sans-serif;"
|
|
face="arial, times new roman" size="-2"><span
|
|
style="text-decoration: underline;"></span></font><font
|
|
face="arial, times new roman" size="-2"><span
|
|
style="font-family: helvetica,arial,sans-serif;">Graphics, &
|
|
Design by </span><a style="font-family: helvetica,arial,sans-serif;"
|
|
href="mailto:willisb@telusplanet.net">Bill Willis</a><span
|
|
style="font-family: helvetica,arial,sans-serif;"> 2001</span><br>
|
|
</font></td>
|
|
</tr>
|
|
</tbody>
|
|
</table>
|
|
</center>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table>
|
|
</center>
|
|
<br>
|
|
<br>
|
|
</body>
|
|
</html>
|