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Determining the equation of a trigonometric function
<?xml version="1.0" encoding="UTF-8"?>
<!--Xholon Workbook http://www.primordion.com/Xholon/wb/ (C) Ken Webb Mon Feb 13 2012 18:01:33 GMT-0500 (EST)-->
<XholonWorkbook>
<Notes><![CDATA[
Khan Academy
------------
Title: Determining the equation of a trigonometric function
Description: Determining the amplitude and period of sine and cosine functions.
Url: http://www.khanacademy.org/video/determining-the-equation-of-a-trigonometric-function?playlist=Trigonometry
InternalName: determining-the-equation-of-a-trigonometric-function
YoutubeId: yvW5l9W1hgE
Keywords: Period, amplitude, sine, cosine, sin, cos, trigonometry, CC_39336_F-IF_7_e
Problem 1 0:00
---------
start with a graph of a sine or cosine curve
sin(0) = 0 and cos(0) = 1
there must be a coefficient, which is the amplitude A of the curve
f(x) = (3/2) * cos(2*PI / pX), where pX is the period of X, and amplitude is 3/2 = 1.5
how many radians until the graph starts repeating? period = 4 * PI
f(x) = 3/2 * cos((2*PI / 4*PI) * x) = 1.5 * (cos(0.5 * x))
Problem 2 5:15
---------
A = 1
this is a sine function
cycles 4 times in 2PI radians, so the period is 4; the coefficient of the x term
f(x) = 1 * sin(4x)
Problem 3 7:15
---------
A = 0.5
cycles 0.5 times in 2PI radians
period = 4PI
f(0) = 0
f(x) = 0.5 * sin(0.5x)
]]></Notes>
<script implName="lang:python:inline:"><![CDATA[
print "TODO"
]]></script>
<script implName="lang:javascript:inline:"><![CDATA[
// Problem 1 - calculate f(x) for one value of x
// I've run it for these values of x to confirm it agrees with Sal's video
// 0 PI 2PI 3PI 4PI -PI -2PI -3PI -4PI
var x = 0;
var a = 1.5;
var p = 4 * Math.PI;
var twoPI = 2 * Math.PI;
var f = a * Math.cos((twoPI / p) * x);
print("f(" + x + ") = " + f + "\n");
// Problem 2
x = 0;
print(1 * Math.sin(4 * x) + "\n");
// Problem 3
x = 0;
print(0.5 * Math.sin(0.5 * x) + "\n");
]]></script>
<_-.XholonClass>
<!-- domain objects -->
<TrigSystem/>
<Problem/>
<X/>
<Amplitude/>
<Period/> <!-- 4PI -->
<Y/>
<!-- quantities -->
<!-- I'll assume all the quantities are dimensionless scalars -->
</_-.XholonClass>
<xholonClassDetails>
<Problem>
<port name="x" connector="#xpointer(X)"/>
<port name="a" connector="#xpointer(Amplitude)"/>
<port name="p" connector="#xpointer(Period)"/>
<port name="twoPI" connector="#xpointer(../Constants/TwoPi)"/>
<port name="y" connector="#xpointer(Y)"/>
</Problem>
<!-- X and Y are passive objects that will be graphed -->
<X xhType="XhtypePurePassiveObject"/>
<Y xhType="XhtypePurePassiveObject"/>
</xholonClassDetails>
<TrigSystem>
<Problem roleName="one">
<X>0.0</X>
<Amplitude>1.5</Amplitude>
<Period/>
<Y>0.0</Y>
<OneProblembehavior implName="org.primordion.script.Behavior_javascript"><![CDATA[
var behaviorObject = new Object();
behaviorObject.postConfigure = function() {
var app = applicationKey;
app.setUseDataPlotter('JFreeChart');
app.setDataPlotterParams('Graph of trig function f(x) = 1.5 * (cos(0.5 * x)),Time (timesteps),X Y,./statistics/,stats,1,WRITE_AS_LONG');
app.createChart(contextNodeKey.getParentNode());
p.setVal(4 * Math.PI);
}
behaviorObject.act = function() {
x.setVal(x.val + 0.1); // try the next value of x
var f = a.val * Math.cos((twoPI.val / p.val) * x.val);
y.setVal(f);
}]]></OneProblembehavior>
</Problem>
<Constants>
<!-- these are available thru JScience -->
<Pi/>
<HalfPi/>
<TwoPi/>
<FourPi/>
</Constants>
</TrigSystem>
<OneProblembehavior implName="org.primordion.script.Behavior_javascript"><![CDATA[]]></OneProblembehavior>
<OneProblembehavior implName="lang:javascript:inline:"><![CDATA[
// As an optional test, paste in as a last child of Problem one.
p.setVal(4 * Math.PI);
var f = a.val * Math.cos((twoPI.val / p.val) * x.val);
y.setVal(f);
print("f(" + x.val + ") = " + y.val + "\n");
]]></OneProblembehavior>
<Blockbehavior implName="lang:bsh:inline:"><![CDATA[]]></Blockbehavior>
<Blockbehavior implName="lang:jruby:inline:"><![CDATA[]]></Blockbehavior>
<Blockbehavior implName="lang:groovy:inline:"><![CDATA[]]></Blockbehavior>
<SvgClient><Attribute_String roleName="svgUri"><![CDATA[data:image/svg+xml,
]]></Attribute_String><Attribute_String roleName="setup">${MODELNAME_DEFAULT},${SVGURI_DEFAULT}</Attribute_String></SvgClient>
</XholonWorkbook>
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