Determining the equation of a trigonometric function

xholonWorkbook.xml

<?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>