<?xml version="1.0" encoding="UTF-8"?>
<quiz>
  <question type="stack">
    <name>
      <text>6.3.3 (Complete parametric table trig 1)</text>
    </name>
    <questiontext format="html">
      <text><![CDATA[<p>Complete the table of coordinates for the curve given in parametric form by \(x = {@xvara@}\) and \(y = {@yvar@}\).</p>
<p></p>
<table style="text-align: center; margin-left:auto; margin-right:auto;" cellpadding="10" bordercolor="#3a87ad" border="1">
<thead>
<tr style="background: #c1ddea">
<th scope="col">\(t\)</th>
<th scope="col">\(x\)</th>
<th scope="col">\(y\)</th>
</tr>
</thead>
<tbody>
<tr>
<td>\(-2\)</td>
<td>[[input:ans21]][[validation:ans21]]</td>
<td>[[input:ans22]]&nbsp;[[validation:ans22]]</td>
</tr>
<tr>
<td>\(-1\)</td>
<td>[[input:ans31]][[validation:ans31]]</td>
<td>[[input:ans32]][[validation:ans32]]</td>
</tr>
<tr>
<td>\(0\)</td>
<td>[[input:ans41]]&nbsp; [[validation:ans41]]</td>
<td>[[input:ans42]][[validation:ans42]]</td>
</tr>
<tr>
<td>\(1\)</td>
<td>[[input:ans51]][[validation:ans51]]</td>
<td>[[input:ans52]][[validation:ans52]]</td>
</tr>
<tr>
<td>\(2\)</td>
<td>[[input:ans61]][[validation:ans61]]</td>
<td>[[input:ans62]]&nbsp; [[validation:ans62]]</td>
</tr>
</tbody>
</table><p>&nbsp;&nbsp; <br></p><p></p>]]></text>
    </questiontext>
    <generalfeedback format="html">
      <text><![CDATA[<p>We simply substitute the values \(t=-2,-1,0,1,2\) into the two expressions \(x = {@xvara@}\) and \(y={@yvar@}\) to get the coordinates \((x,y)\) at each value of \(t\).&nbsp; Thus</p><table style="text-align: center; margin-left:auto; margin-right:auto;" cellpadding="10" bordercolor="#3a87ad" border="1">
<thead>
<tr style="background: #c1ddea">
<th scope="col">\(t\)</th>
<th scope="col">\(x\)</th>
<th scope="col">\(y\)</th>
</tr>
</thead>
<tbody>
<tr>
<td>\(-2\)</td>
<td>{@ta21@}</td>
<td>{@ta22@}</td>
</tr>
<tr>
<td>\(-1\)</td>
<td>{@ta31@}</td>
<td>{@ta32@}</td>
</tr>
<tr>
<td>\(0\)</td>
<td>{@ta41@}</td>
<td>{@ta42@}</td>
</tr>
<tr>
<td>\(1\)</td>
<td>{@ta51@}</td>
<td>{@ta52@}</td>
</tr>
<tr>
<td>\(2\)</td>
<td>{@ta61@}</td>
<td>{@ta62@}</td>
</tr>
</tbody>
</table>]]></text>
    </generalfeedback>
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    <hidden>0</hidden>
    <idnumber/>
    <stackversion>
      <text>2020081700</text>
    </stackversion>
    <questionvariables>
      <text>sind(d):=sin(d*%pi/180);
asind(x):=asin(x)*180/%pi;

a:1+rand(4);
b:1+rand(4);
c:1+rand(4);
d:1+rand(4);

xvara: a + b*sin(t*90);
xvar: a + b*sind(t*90);

yvar:c*t^2 -d;
ta11:ev(xvar,t=-3);
ta21:ev(xvar,t=-2);
ta31:ev(xvar,t=-1);
ta41:ev(xvar,t=0);
ta51:ev(xvar,t=1);
ta61:ev(xvar,t=2);
ta71:ev(xvar,t=3);
ta12:ev(yvar,t=-3);
ta22:ev(yvar,t=-2);
ta32:ev(yvar,t=-1);
ta42:ev(yvar,t=0);
ta52:ev(yvar,t=1);
ta62:ev(yvar,t=2);
ta72:ev(yvar,t=3);</text>
    </questionvariables>
    <specificfeedback format="html">
      <text>[[feedback:prt1]]</text>
    </specificfeedback>
    <questionnote format="moodle_auto_format">
      <text>{@xvara@} and {@yvar@}</text>
    </questionnote>
    <questiondescription format="moodle_auto_format">
      <text/>
    </questiondescription>
    <questionsimplify>1</questionsimplify>
    <assumepositive>0</assumepositive>
    <assumereal>0</assumereal>
    <prtcorrect format="html">
      <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Correct answer, well done.]]></text>
    </prtcorrect>
    <prtpartiallycorrect format="html">
      <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Your answer is partially correct.]]></text>
    </prtpartiallycorrect>
    <prtincorrect format="html">
      <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Incorrect answer.]]></text>
    </prtincorrect>
    <decimals>.</decimals>
    <scientificnotation>*10</scientificnotation>
    <multiplicationsign>none</multiplicationsign>
    <sqrtsign>1</sqrtsign>
    <complexno>i</complexno>
    <inversetrig>cos-1</inversetrig>
    <logicsymbol>lang</logicsymbol>
    <matrixparens>[</matrixparens>
    <isbroken>0</isbroken>
    <variantsselectionseed/>
    <input>
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      <type>algebraic</type>
      <tans>ta21</tans>
      <boxsize>5</boxsize>
      <strictsyntax>1</strictsyntax>
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      <tans>ta31</tans>
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      <options/>
    </input>
    <input>
      <name>ans32</name>
      <type>algebraic</type>
      <tans>ta32</tans>
      <boxsize>5</boxsize>
      <strictsyntax>1</strictsyntax>
      <insertstars>0</insertstars>
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      <tans>ta41</tans>
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      <strictsyntax>1</strictsyntax>
      <insertstars>0</insertstars>
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      <tans>ta42</tans>
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      <strictsyntax>1</strictsyntax>
      <insertstars>0</insertstars>
      <syntaxhint/>
      <syntaxattribute>0</syntaxattribute>
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      <options/>
    </input>
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      <name>ans51</name>
      <type>algebraic</type>
      <tans>ta51</tans>
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      <options/>
    </input>
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      <name>ans52</name>
      <type>algebraic</type>
      <tans>ta52</tans>
      <boxsize>5</boxsize>
      <strictsyntax>1</strictsyntax>
      <insertstars>0</insertstars>
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      <type>algebraic</type>
      <tans>ta61</tans>
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      <strictsyntax>1</strictsyntax>
      <insertstars>0</insertstars>
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      <options/>
    </input>
    <input>
      <name>ans62</name>
      <type>algebraic</type>
      <tans>ta62</tans>
      <boxsize>5</boxsize>
      <strictsyntax>1</strictsyntax>
      <insertstars>0</insertstars>
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      <feedbackvariables>
        <text>test:(ans21-ta21)^2+(ans22-ta22)^2+(ans31-ta31)^2+(ans32-ta32)^2+(ans41-ta41)^2+(ans42-ta42)^2+(ans51-ta51)^2+(ans52-ta52)^2+(ans61-ta61)^2+(ans62-ta62)^2</text>
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        <sans>ans21</sans>
        <tans>ta21</tans>
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        <truescore>0.1000000</truescore>
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        <truenextnode>1</truenextnode>
        <trueanswernote>prt1-1-T</trueanswernote>
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          <text/>
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      <node>
        <name>1</name>
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        <answertest>AlgEquiv</answertest>
        <sans>ans22</sans>
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        <truenextnode>2</truenextnode>
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        <answertest>AlgEquiv</answertest>
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        <name>4</name>
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        <answertest>AlgEquiv</answertest>
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      <testinput>
        <name>ans21</name>
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        <name>ans22</name>
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        <value>ta52</value>
      </testinput>
      <testinput>
        <name>ans61</name>
        <value>ta61</value>
      </testinput>
      <testinput>
        <name>ans62</name>
        <value>ta62</value>
      </testinput>
      <expected>
        <name>prt1</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prt1-10-T</expectedanswernote>
      </expected>
    </qtest>
    <qtest>
      <testcase>2</testcase>
      <description/>
      <testinput>
        <name>ans21</name>
        <value>ta21</value>
      </testinput>
      <testinput>
        <name>ans22</name>
        <value>ta22</value>
      </testinput>
      <testinput>
        <name>ans31</name>
        <value>ta31</value>
      </testinput>
      <testinput>
        <name>ans32</name>
        <value>ta32</value>
      </testinput>
      <testinput>
        <name>ans41</name>
        <value>ta41</value>
      </testinput>
      <testinput>
        <name>ans42</name>
        <value>ta42</value>
      </testinput>
      <testinput>
        <name>ans51</name>
        <value>ta51</value>
      </testinput>
      <testinput>
        <name>ans52</name>
        <value>1+ta52</value>
      </testinput>
      <testinput>
        <name>ans61</name>
        <value>ta61</value>
      </testinput>
      <testinput>
        <name>ans62</name>
        <value>ta62</value>
      </testinput>
      <expected>
        <name>prt1</name>
        <expectedscore>0.9000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prt1-10-T</expectedanswernote>
      </expected>
    </qtest>
  </question>
</quiz>
