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fix part c and improve intro and part d #69

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Merged
mattboelkins merged 1 commit into from
Sep 20, 2026
Merged

fix part c and improve intro and part d #69

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31 changes: 18 additions & 13 deletions source/previews/doenet/PA-circular-sine-D.doenetml
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Original file line number Diff line number Diff line change
Expand Up @@ -21,7 +21,8 @@
<point>(cos($anglelist[$k]),sin($anglelist[$k]))</point>
</repeatForSequence>

<mathList name="tsEnt">$listEnt</mathList>
<!-- <mathList name="tsEnt">$listEnt</mathList> -->
<mathList name="tsEnt"><convertSetToList>{$listEnt}</convertSetToList></mathList>
<number name="ans">-sqrt(3)/2</number>

<repeatForSequence name="bools" from="1" to="16" valueName="n">
Expand Down Expand Up @@ -91,6 +92,10 @@

</setup>

<p>
If we consider the unit circle, start at <m>t = 0</m>, and traverse the circle counterclockwise, we may view the height, <m>h</m>, of the traversing point as a function of the angle, <m>t</m>, in radians. From there, we can plot the resulting <m>(t,h)</m> ordered pairs and connect them to generate the circular function <m>f(t)</m> pictured in the following figure. This function tracks the height of a point traversing the unit circle, so that <m>h=f(t)</m> is the height of the point at angle <m>t</m>.
</p>

<sideBySide widths="40% 60%">
<graph xMin="-1.5" xMax="1.5" yMin="-1.5" yMax="1.5" displayXAxisTicks="false" displayYAxisTicks="false" fixAxes yLabelAlignment="right">
<shortDescription>graph of a unit circle and moveable point on the circle</shortDescription>
Expand Down Expand Up @@ -155,64 +160,64 @@
<p>
Complete the following table with the exact values of <m>h</m> that correspond to the stated inputs.
</p>
<tabular bottom="minor" top="minor">
<row bottom="minor" halign="center">
<tabular bottomBorder="minor" topBorder="minor">
<row bottomBorder="minor" halign="center">
<cell><m>t</m></cell>
<cell><m>0</m></cell>
<cell><m>$anglelist[1]</m></cell>
<cell><m>$anglelist[2]</m></cell>
<cell><m>$anglelist[3]</m></cell>
<cell><m>$anglelist[4]</m></cell>
</row>
<row halign="center" bottom="major">
<row halign="center" bottomBorder="major">
<cell><m>h</m></cell>
<cell><answer><mathInput minWidth="40"><shortDescription>value of h</shortDescription></mathInput>0</answer></cell>
<cell><answer><mathInput minWidth="40"><shortDescription>value of h</shortDescription></mathInput>$plist[1][2]</answer></cell>
<cell><mathInput minWidth="40" disabled><shortDescription>value of h</shortDescription><conditionalContent condition="$fpiover4.creditAchieved=1">$plist[2][2]</conditionalContent></mathInput></cell>
<cell><mathInput minWidth="40" disabled><shortDescription>value of h</shortDescription><conditionalContent condition="$fpiover3.creditAchieved=1">$plist[3][2]</conditionalContent></mathInput></cell>
<cell><answer><mathInput minWidth="40"><shortDescription>value of h</shortDescription></mathInput>$plist[4][2]</answer></cell>
</row>
<row bottom="minor" halign="center">
<row bottomBorder="minor" halign="center">
<cell><m>t</m></cell>
<cell><m>$anglelist[5]</m></cell>
<cell><m>$anglelist[6]</m></cell>
<cell><m>$anglelist[7]</m></cell>
<cell><m>$anglelist[8]</m></cell>
<cell><m>$anglelist[9]</m></cell>
</row>
<row halign="center" bottom="major">
<row halign="center" bottomBorder="major">
<cell><m>h</m></cell>
<cell><answer><mathInput minWidth="40"><shortDescription>value of h</shortDescription></mathInput>$plist[5][2]</answer></cell>
<cell><answer><mathInput minWidth="40"><shortDescription>value of h</shortDescription></mathInput>$plist[6][2]</answer></cell>
<cell><answer><mathInput minWidth="40"><shortDescription>value of h</shortDescription></mathInput>$plist[7][2]</answer></cell>
<cell><answer><mathInput minWidth="40"><shortDescription>value of h</shortDescription></mathInput>$plist[8][2]</answer></cell>
<cell><answer><mathInput minWidth="40"><shortDescription>value of h</shortDescription></mathInput>$plist[9][2]</answer></cell>
</row>
<row bottom="minor" halign="center">
<row bottomBorder="minor" halign="center">
<cell><m>t</m></cell>
<cell><m>$anglelist[10]</m></cell>
<cell><m>$anglelist[11]</m></cell>
<cell><m>$anglelist[12]</m></cell>
<cell><m>$anglelist[13]</m></cell>
<cell><m>$anglelist[14]</m></cell>
</row>
<row halign="center" bottom="major">
<row halign="center" bottomBorder="major">
<cell><m>h</m></cell>
<cell><answer><mathInput minWidth="40"><shortDescription>value of h</shortDescription></mathInput>$plist[10][2]</answer></cell>
<cell><answer><mathInput minWidth="40"><shortDescription>value of h</shortDescription></mathInput>$plist[11][2]</answer></cell>
<cell><answer><mathInput minWidth="40"><shortDescription>value of h</shortDescription></mathInput>$plist[12][2]</answer></cell>
<cell><answer><mathInput minWidth="40"><shortDescription>value of h</shortDescription></mathInput>$plist[13][2]</answer></cell>
<cell><answer><mathInput minWidth="40"><shortDescription>value of h</shortDescription></mathInput>$plist[14][2]</answer></cell>
</row>
<row bottom="minor" halign="center">
<row bottomBorder="minor" halign="center">
<cell><m>t</m></cell>
<cell><m>$anglelist[15]</m></cell>
<cell><m>$anglelist[16]</m></cell>
<cell></cell>
<cell></cell>
<cell></cell>
</row>
<row halign="center" bottom="major">
<row halign="center" bottomBorder="major">
<cell><m>h</m></cell>
<cell><answer><mathInput minWidth="40"><shortDescription>value of h</shortDescription></mathInput>$plist[15][2]</answer></cell>
<cell><answer><mathInput minWidth="40"><shortDescription>value of h</shortDescription></mathInput>$plist[16][2]</answer></cell>
Expand All @@ -228,11 +233,11 @@
</p>
<p>
What is the exact value of <m>f\left(\frac{11\pi}{4}\right)?</m><br/>
<answer><label><m>f\left(\frac{11\pi}{4}\right)=</m></label>-sqrt(2)/2</answer>
<answer><label><m>f\left(\frac{11\pi}{4}\right)=</m></label>sqrt(2)/2</answer>
</p>
<p>
What is the exact value of <m>f\left(\frac{14\pi}{3}\right)?</m><br/>
<answer><label><m>f\left(\frac{14\pi}{3}\right)=</m></label>-sqrt(3)/2</answer>
<answer><label><m>f\left(\frac{14\pi}{3}\right)=</m></label>sqrt(3)/2</answer>
</p>
</li>
<li>
Expand All @@ -242,4 +247,4 @@
</p>
</li>

</ol>
</ol>
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