e39465ad2f
new file: Files/flashplayer_32_sa.exe
new file: favicon.ico
new file: globe.gif
new file: imgs/download.png
new file: imgs/zuck.jpg
new file: index.html
new file: other.ico
new file: script.js
new file: site.webmanifest
new file: sitemap.html
new file: styles/backround.css
new file: styles/border.css
new file: styles/fonts/Titillium_Web/OFL.txt
new file: styles/fonts/Titillium_Web/TitilliumWeb-Black.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-Bold.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-BoldItalic.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-ExtraLight.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-ExtraLightItalic.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-Italic.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-Light.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-LightItalic.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-Regular.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-SemiBold.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-SemiBoldItalic.ttf
new file: styles/fonts/webfontkit-20221027-163353/generator_config.txt
new file: styles/fonts/webfontkit-20221027-163353/specimen_files/grid_12-825-55-15.css
new file: styles/fonts/webfontkit-20221027-163353/specimen_files/specimen_stylesheet.css
new file: styles/fonts/webfontkit-20221027-163353/stylesheet.css
new file: styles/fonts/webfontkit-20221027-163353/titilliumweb-extralight-demo.html
new file: styles/fonts/webfontkit-20221027-163353/titilliumweb-extralight-webfont.woff
new file: styles/fonts/webfontkit-20221027-163353/titilliumweb-extralight-webfont.woff2
new file: styles/fonts/webfontkit-20221027-165950/generator_config.txt
new file: styles/fonts/webfontkit-20221027-165950/specimen_files/grid_12-825-55-15.css
new file: styles/fonts/webfontkit-20221027-165950/specimen_files/specimen_stylesheet.css
new file: styles/fonts/webfontkit-20221027-165950/stylesheet.css
new file: styles/fonts/webfontkit-20221027-165950/titilliumweb-bold-demo.html
new file: styles/fonts/webfontkit-20221027-165950/titilliumweb-bold-webfont.woff
new file: styles/fonts/webfontkit-20221027-165950/titilliumweb-bold-webfont.woff2
new file: styles/style.css
new file: tools/2048/.gitignore
new file: tools/2048/.jshintrc
new file: tools/2048/CONTRIBUTING.md
new file: tools/2048/LICENSE.txt
new file: tools/2048/README.md
new file: tools/2048/Rakefile
new file: tools/2048/favicon.ico
new file: tools/2048/index.html
new file: tools/2048/js/animframe_polyfill.js
new file: tools/2048/js/application.js
new file: tools/2048/js/bind_polyfill.js
new file: tools/2048/js/classlist_polyfill.js
new file: tools/2048/js/game_manager.js
new file: tools/2048/js/grid.js
new file: tools/2048/js/html_actuator.js
new file: tools/2048/js/keyboard_input_manager.js
new file: tools/2048/js/local_storage_manager.js
new file: tools/2048/js/tile.js
new file: tools/2048/meta/apple-touch-icon.png
new file: tools/webretro/cores/neocd_libretro.js
new file: tools/webretro/cores/neocd_libretro.wasm
new file: tools/webretro/cores/nestopia_libretro.js
new file: tools/webretro/cores/nestopia_libretro.wasm
new file: tools/webretro/cores/o2em_libretro.js
new file: tools/webretro/cores/o2em_libretro.wasm
new file: tools/webretro/cores/opera_libretro.js
new file: tools/webretro/cores/opera_libretro.wasm
230 lines
9.4 KiB
HTML
230 lines
9.4 KiB
HTML
<!doctype html>
|
|
<html lang="en"><!-- #BeginTemplate "/Templates/Main.dwt" --><!-- DW6 -->
|
|
|
|
<!-- Mirrored from www.mathsisfun.com/geometry/radians.html by HTTrack Website Copier/3.x [XR&CO'2014], Sat, 29 Oct 2022 00:43:14 GMT -->
|
|
<head>
|
|
<!-- #BeginEditable "doctitle" -->
|
|
<title>Radians</title>
|
|
<script language="JavaScript" type="text/javascript">reSpell=[["center","centre"]];</script>
|
|
<!-- #EndEditable -->
|
|
<meta name="keywords" content="math, maths, mathematics, school, homework, education">
|
|
<meta http-equiv="content-type" content="text/html; charset=utf-8">
|
|
<meta name="viewport" content="width=device-width, initial-scale=1.0, user-scalable=yes">
|
|
<meta name="HandheldFriendly" content="true">
|
|
<meta http-equiv="pics-label" content='(PICS-1.1 "http://www.classify.org/safesurf/" L gen true for "http://www.mathsisfun.com" r (SS~~000 1))'>
|
|
<link rel="stylesheet" type="text/css" href="../style3.css" />
|
|
<script src="../main3.js" type="text/javascript"></script>
|
|
</head>
|
|
|
|
<body id="bodybg">
|
|
<div class="bg">
|
|
<div id="stt"></div>
|
|
<div id="hdr"></div>
|
|
<div id="logo"><a href="../index.html"><img src="../images/style/logo.svg" alt="Math is Fun" /></a></div>
|
|
<div id="gtran"><script type="text/javascript">document.write(getTrans());</script></div>
|
|
<div id="gplus"><script type="text/javascript">document.write(getGPlus());</script></div>
|
|
<div id="adTopOuter" class="centerfull noprint">
|
|
<div id="adTop">
|
|
<script type="text/javascript">document.write(getAdTop());</script>
|
|
</div>
|
|
</div>
|
|
<div id="adHide">
|
|
<div id="showAds1"><a href="javascript:showAds()">Show Ads</a></div>
|
|
<div id="hideAds1"><a href="javascript:hideAds()">Hide Ads</a><br>
|
|
<a href="../about-ads.html">About Ads</a></div>
|
|
</div>
|
|
<div id="menuWide" class="menu">
|
|
<script type="text/javascript">document.write(getMenu(0));</script>
|
|
</div>
|
|
<div id="linkto">
|
|
<div id="linktort"><script type="text/javascript">document.write(getLinks());</script></div>
|
|
</div>
|
|
<div id="search" role="search"><script type="text/javascript">document.write(getSearch());</script></div>
|
|
<div id="menuSlim" class="menu">
|
|
<script type="text/javascript">document.write(getMenu(1));</script>
|
|
</div>
|
|
<div id="menuTiny" class="menu">
|
|
<script type="text/javascript">document.write(getMenu(2));</script>
|
|
</div>
|
|
<div id="extra"></div>
|
|
</div>
|
|
<div id="content" role="main"><!-- #BeginEditable "Body" -->
|
|
|
|
<h1 align="center">Radians</h1>
|
|
|
|
<p class="center"><i>The angle made when the radius <br>
|
|
is
|
|
wrapped round the circle:</i></p>
|
|
<p class="center"><img src="images/radian-circle.svg" alt="radian in circle" /></p>
|
|
<table border="0" align="center">
|
|
<tr>
|
|
<td><img src="images/radian.svg" alt="1 radian is about 57.2958 degrees" /></td>
|
|
<td width="20"> </td>
|
|
<td><p>1 Radian is <i>about</i> 57.2958 <a href="degrees.html">degrees</a>. </p></td>
|
|
</tr>
|
|
</table>
|
|
<p class="center"><i>Why "57.2958..." degrees?</i> We will see in a moment.</p>
|
|
<p class="larger">The <b>Radian</b> is a pure measure based on the <b>Radius</b> of the circle:</p>
|
|
|
|
|
|
<iframe src="iradian.html" scrolling="no" style="width:362px; height:282px; overflow:hidden; margin:auto; display:block; border:none;"></iframe>
|
|
|
|
<p class="center larger"><b>Radian</b>: the angle made when we take the <b>radius</b> <br />
|
|
and wrap it round the circle.</p>
|
|
|
|
<!-- <div class="flash">
|
|
<script type="text/javascript">putFlash6(400,378,'images/radians.swf','','#FFFFFF');</script>
|
|
<noscript>
|
|
<object type="application/x-shockwave-flash" width="400" height="378" data="images/radians.swf" align="middle">
|
|
<param name="allowScriptAccess" value="sameDomain" />
|
|
<param name="allowFullScreen" value="true" />
|
|
<param name="movie" value="images/radians.swf" />
|
|
<param name="quality" value="high" />
|
|
<param name="bgcolor" value="#FFFFFF" />
|
|
</object>
|
|
</noscript>
|
|
</div>
|
|
-->
|
|
|
|
|
|
<div style="clear:both"></div>
|
|
<h2>Radians and Degrees </h2>
|
|
<p>Let us see why 1 Radian is equal to 57.2958... degrees:</p>
|
|
|
|
|
|
<iframe src="iradian-circ.html" scrolling="no" style="width:362px; height:282px; overflow:hidden; margin:auto; display:block; border:none;"></iframe>
|
|
|
|
|
|
<p style="float:left; margin: 0 10px 5px 0;"><img src="../numbers/images/pi-circle.gif" width="172" height="188" alt="radius of 1, pi is half of circumference" /></p>
|
|
|
|
<p>In a half circle there are
|
|
|
|
<span class="larger"><span class="times">π</span> radians</span>, which is also <span class="larger">180°</span></p><div class="tbl">
|
|
<div class="row"><span class="left"><span class="large center"><span class="times">π</span> radians =</span></span><span class="right"><span class="large center">180°</span></span></div>
|
|
<div class="row"><span class="left"><span class="large center">So <b>1 radian</b> = </span></span><span class="right"><span class="large center">180°/<span class="times">π</span></span></span></div>
|
|
<div class="row"><span class="left">=</span><span class="right"><span class="large center">57.2958...°</span></span></div>
|
|
<div class="row"><span class="left"> </span><span class="right"><span class="large center"> (approximately)</span></span></div>
|
|
</div>
|
|
<p>To go from <b>radians to degrees</b>: multiply by 180, divide by <span class="times">π</span></p>
|
|
<p>To go from <b>degrees to radians</b>: multiply by <span class="times">π</span>, divide by 180</p>
|
|
<p>Here is a table of equivalent values:</p>
|
|
|
|
<div class="simple">
|
|
<table align="center">
|
|
<tr align="center">
|
|
<th>Degrees </th>
|
|
<th>Radians<br />
|
|
(exact)</th>
|
|
<th>Radians<br />
|
|
(approx)</th>
|
|
</tr>
|
|
<tr align="center">
|
|
<td>30°</td>
|
|
<td><span class="times">π</span>/6</td>
|
|
<td>0.524</td>
|
|
</tr>
|
|
<tr align="center">
|
|
<td>45°</td>
|
|
<td><span class="times">π</span>/4</td>
|
|
<td>0.785</td>
|
|
</tr>
|
|
<tr align="center">
|
|
<td>60°</td>
|
|
<td><span class="times">π</span>/3</td>
|
|
<td>1.047</td>
|
|
</tr>
|
|
<tr align="center">
|
|
<td>90°</td>
|
|
<td><span class="times">π</span>/2</td>
|
|
<td>1.571</td>
|
|
</tr>
|
|
<tr align="center">
|
|
<td>180°</td>
|
|
<td><span class="times">π</span></td>
|
|
<td>3.142</td>
|
|
</tr>
|
|
<tr align="center">
|
|
<td>270°</td>
|
|
<td>3<span class="times">π</span>/2</td>
|
|
<td>4.712</td>
|
|
</tr>
|
|
<tr align="center">
|
|
<td>360°</td>
|
|
<td>2<span class="times">π</span></td>
|
|
<td>6.283</td>
|
|
</tr>
|
|
</table>
|
|
<p> </p>
|
|
</div>
|
|
|
|
<div class="example">
|
|
<p style="float:right; margin: 0 0 5px 10px;"><img src="images/radian-string.svg" alt="radians circle 6.28... pieces of string" /></p>
|
|
<h3>Example: How Many Radians in a <a href="full-rotation.html">Full Circle</a>? </h3>
|
|
<p>Imagine you cut pieces of string exactly the length from the <b>center to the circumference of a circle</b> ... </p>
|
|
<p>... how many pieces do you need to go <b>once around </b> the circle? </p>
|
|
<p> </p>
|
|
<p class="center larger">Answer: 2<span class="times">π</span> (or about <b>6.283</b> pieces of string). </p>
|
|
</div>
|
|
<h2>Radians Preferred by Mathematicians</h2>
|
|
<p>Because the radian is based on the pure idea of <i>"the radius being laid along the circumference</i>", it often gives simple and natural results when used in mathematics.</p>
|
|
<p><b>For example</b>, look at the <a href="../sine-cosine-tangent.html">sine function</a> for very small values:</p>
|
|
<div class="simple">
|
|
<table align="center">
|
|
<tr>
|
|
<th width="116">x
|
|
(radians)</th>
|
|
<td width="116" height="18">1</td>
|
|
<td width="102" height="18">0.1</td>
|
|
<td width="77" height="18">0.01</td>
|
|
<td width="77">0.001</td>
|
|
</tr>
|
|
<tr>
|
|
<th>sin(x)</th>
|
|
<td>0.8414710</td>
|
|
<td>0.0998334</td>
|
|
<td>0.0099998</td>
|
|
<td>0.0009999998</td>
|
|
</tr>
|
|
</table>
|
|
<br />
|
|
</div>
|
|
|
|
<div align="center"><span class="larger">For very small values. "x" and "sin(x)" are almost the same</span><br />
|
|
(as long as "x" is in Radians!)
|
|
</div>
|
|
<br />
|
|
|
|
<p>There will be other examples like that as you learn more about mathematics. </p>
|
|
<h2>Conclusion</h2>
|
|
<p>So, degrees are easier to use in everyday work, but radians are much better for mathematics.</p>
|
|
<p> </p>
|
|
|
|
<div class="questions">
|
|
<script type="text/javascript">getQ(7436, 7437, 7438, 7439, 7440, 7441, 7442, 7443, 7444, 7445);</script>
|
|
</div>
|
|
|
|
|
|
<div class="related">
|
|
<a href="degrees.html">Degrees</a>
|
|
<a href="plane.html">Plane</a>
|
|
<a href="../numbers/pi.html">Pi</a>
|
|
<a href="steradian.html">Steradian</a>
|
|
<a href="symbols.html">Symbols in Geometry</a>
|
|
<a href="index.html">Geometry Index</a></div>
|
|
<!-- #EndEditable --></div>
|
|
<div id="adend" class="centerfull noprint">
|
|
<script type="text/javascript">document.write(getAdEnd());</script>
|
|
</div>
|
|
<div id="footer" class="centerfull noprint">
|
|
<script type="text/javascript">document.write(getFooter());</script>
|
|
</div>
|
|
<div id="copyrt">
|
|
Copyright © 2017 MathsIsFun.com
|
|
</div>
|
|
|
|
<script type="text/javascript">document.write(getBodyEnd());</script>
|
|
</body>
|
|
<!-- #EndTemplate -->
|
|
<!-- Mirrored from www.mathsisfun.com/geometry/radians.html by HTTrack Website Copier/3.x [XR&CO'2014], Sat, 29 Oct 2022 00:43:15 GMT -->
|
|
</html>
|