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Kathy first draft for TR1 #357

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0f3ad54
Kathy first draft for TR1
kathypinzon Oct 15, 2024
f38b336
Fix xml ids and one image
siwelwerd Oct 15, 2024
64822fd
Fix some images
siwelwerd Oct 15, 2024
3848573
Add little arc to angle
siwelwerd Oct 15, 2024
5844cd7
2nd update to TR1
kathypinzon Oct 29, 2024
97219fa
xmlids cannot start with a number
siwelwerd Oct 29, 2024
7345231
Discard changes to .vscode/settings.json
siwelwerd Oct 29, 2024
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302 changes: 302 additions & 0 deletions source/precalculus/source/06-TR/01.ptx
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Original file line number Diff line number Diff line change
Expand Up @@ -12,6 +12,308 @@
<subsection>
<title>Activities</title>

<definition xml:id="angle"> An <term>angle</term> is formed by joining two rays at their starting points. The point where they are joined is called the <term> vertex</term> of the angle. The measure of an angle is the amount of a circle between the two rays. </definition>

<activity>
<introduction>
<p>
We know that if you complete a full turn of the circle the angle created will be 360 degrees. Use this to estimate the measure of the given angles.

</p>
</introduction>
<task>
<statement>
<p> <figure xml:id="fig-90-degree-angle"><image width="50%">
<sageplot>
p=arrow((0,0),(3,3),aspect_ratio=1)
p+=arrow((0,0),(-3,3))
p+=arc((0,0),0.5,sector=(pi/4, 3*pi/4),color="black")
p.axes(False)
p
</sageplot>
</image></figure>
<ol marker="A." cols="2">
<li><p><m>45^{\circ}</m> </p></li>
<li><p> <m>90^{\circ}</m> </p></li>
<li><p> <m>135^{\circ}</m> </p></li>
<li><p> <m>180^{\circ}</m></p></li>
</ol> </p>
</statement>
<answer>
<p>
B
</p>
</answer>
</task>
<task>
<statement>
<figure><image width="50%">
<sageplot>
p=arrow((0,0),(-4,1),aspect_ratio=1)
p+=arrow((0,0),(4,-1))
p+=point((0,0),size=50)
p+=arc((0,0),0.5,sector=(atan(-1/4), atan(-1/4)+pi),color="black")
p.axes(False)
p
</sageplot>
</image></figure>
<p>
<ol marker="A." cols="2">
<li><p><m>45^{\circ}</m> </p></li>
<li><p> <m>90^{\circ}</m> </p></li>
<li><p> <m>135^{\circ}</m> </p></li>
<li><p> <m>180^{\circ}</m></p></li>
</ol> </p>
</statement>
<answer>
<p>
D
</p>
</answer>
</task>
<task>
<statement>
<p> <figure xml:id="fig-135-degree-angle"><image width="50%">
<sageplot>
p=arrow((0,0),(0,4),aspect_ratio=1)
p+=arrow((0,0),(-3,-3))
p+=arc((0,0),0.5,sector=(pi/2, 5*pi/4),color="black")
p.axes(False)
p
</sageplot>
</image></figure>
<ol marker="A." cols="2">
<li><p><m>45^{\circ}</m> </p></li>
<li><p> <m>90^{\circ}</m> </p></li>
<li><p> <m>135^{\circ}</m> </p></li>
<li><p> <m>180^{\circ}</m></p></li>
</ol> </p>
</statement>
<answer>
<p>
C
</p>
</answer>
</task>
</activity>
<definition>
<statement>
<p>
An angle is in <term>standard position</term> if its vertex is located at the origin and its initial side extends along the positive <m>x</m>-axis.
</p>
</statement>
<figure xml:id="standard-position"><image width="50%">
<sageplot>
p=arrow((0,0),(4,0),aspect_ratio=1)
p+=arrow((0,0),(-3,-3))
p+=arc((0,0),0.5,sector=(0, 5*pi/4),color="black")
p
</sageplot>
</image></figure>
Comment on lines +105 to +112
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@StevenClontz We want to have the axes show up on this one, but no tickmarks or tickmark labels. Do you know how to do that?

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I think I figured it out. The key is to past a list of two empty lists (ticks=[[],[]]), rather than ticks=None like I was trying.

Suggested change
<figure xml:id="standard-position"><image width="50%">
<sageplot>
p=arrow((0,0),(4,0),aspect_ratio=1)
p+=arrow((0,0),(-3,-3))
p+=arc((0,0),0.5,sector=(0, 5*pi/4),color="black")
p
</sageplot>
</image></figure>
<figure xml:id="standard-position"><image width="50%">
<sageplot>
p=arrow((0,0),(4,0),aspect_ratio=1,ticks=[[],[]])
p+=arrow((0,0),(-3,-3))
p+=arc((0,0),0.5,sector=(0, 5*pi/4),color="black")
p
</sageplot>
</image></figure>

<statement>
<p>
An angle measured counterclockwise from the initial side has a positive measure, while an angle measured clockwise from the initial side has a negative measure.
</p>
</statement>
<figure xml:id="standard-position-neg"><image width="50%">
<sageplot>
p=arrow((0,0),(4,0),aspect_ratio=1)
p+=arrow((0,0),(-3,-3))
p+=arc((0,0),0.5,sector=(5*pi/4,2*pi),color="black")
p
</sageplot>
Comment on lines +119 to +124
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@StevenClontz Same for this one

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Suggested change
<sageplot>
p=arrow((0,0),(4,0),aspect_ratio=1)
p+=arrow((0,0),(-3,-3))
p+=arc((0,0),0.5,sector=(5*pi/4,2*pi),color="black")
p
</sageplot>
<sageplot>
p=arrow((0,0),(4,0),aspect_ratio=1,ticks=[[],[]])
p+=arrow((0,0),(-3,-3))
p+=arc((0,0),0.5,sector=(5*pi/4,2*pi),color="black")
p
</sageplot>

</image></figure>

</definition>

<activity>
<introduction>
<p>
Find the measure of the angles drawn in standard position.
</p>
</introduction>
<task>
<statement>
<p> <figure xml:id="fig-45-degree-angle"><image width="50%">
<sageplot>
p=arrow((0,0),(4,0), aspect_ratio=1)
p+=arrow((0,0),(3,3))
p+=arc((0,0),0.5,sector=(0,pi/4),color="black")
p.axes(False)
p
</sageplot>
</image></figure>
<ol marker="A." cols="2">
<li><p><m>45^{\circ}</m> </p></li>
<li><p> <m>90^{\circ}</m> </p></li>
<li><p> <m>135^{\circ}</m> </p></li>
<li><p> <m>180^{\circ}</m></p></li>
</ol> </p>
</statement>
<answer>
<p>
A
</p>
</answer>
</task>
<task>
<statement>
<p> <figure xml:id="fig-180-degree-angle"><image width="50%">
<sageplot>
p=arrow((0,0),(4,0),aspect_ratio=1)
p+=arrow((0,0),(-4,0))
p+=arc((0,0),0.5,sector=(pi,2*pi),color="black")
p.axes(False)
p
</sageplot>
</image></figure>
<ol marker="A." cols="2">
<li><p><m>180^{\circ}</m> </p></li>
<li><p> <m>90^{\circ}</m> </p></li>
<li><p> <m>-180^{\circ}</m> </p></li>
<li><p> <m>-90^{\circ}</m></p></li>
</ol> </p>
</statement>
<answer>
<p>

C
</p>
</answer>
</task>
<task>
<statement>
<p> <figure xml:id="fig-210-degree-angle"><image width="50%">
<sageplot>
p=arrow((0,0),(4,0),aspect_ratio=1)
p+=arrow((0,0),(4*cos(7*pi/6),3*sin(7*pi/6)))
p+=arc((0,0),0.5,sector=(0,7*pi/6),color="black")
p.axes(False)
p
</sageplot>
</image></figure>
<ol marker="A." cols="2">
<li><p><m>30^{\circ}</m> </p></li>
<li><p> <m>-150^{\circ}</m> </p></li>
<li><p> <m>-210^{\circ}</m> </p></li>
<li><p> <m>210^{\circ}</m></p></li>
</ol> </p>
</statement>
<answer>
<p>
D
</p>
</answer>
</task>
<task>
<statement>
<p> Draw an angle of measure <m>-225^{\circ} </m> in standard position.
</p></statement>
<answer>
<figure xml:id="fig-225-degree-angle"><image width="50%">
<sageplot>
p=arrow((0,0),(4,0),aspect_ratio=1)
p+=arrow((0,0),(4*cos(3*pi/4),4*sin(3*pi/4)))
p+=arc((0,0),0.5,sector=(3*pi/4,2*pi),color="black")
p.axes(False)
p
</sageplot>
</image></figure>
</answer>
</task>
</activity>

<remark>
Activity or remark - Something about the circumference of a circle being another way to measure the angle. <m>C=2\pi r</m> divide both sides by the radius, so a full circle or <m>360^{\circ}=2\pi</m> radians
</remark>

<definition xml:id="def-radian">
<statement>
<p>
One <term>radian</term> is the measure of a central angle of a circle that intersects an arc the same length as the radius.
</p>
</statement>
</definition>

<activity>
<introduction>
<p>
Using the fact that one turn around the circle is <m>360^{\circ}</m> and also <m>2\pi</m> radians. Find the measure of the following angles in radians.
</p>
</introduction>
<task>
<statement>
<p> <m>180^{\circ}</m>
<ol marker="A." cols="2">
<li><p> <m>\frac{\pi}{4}</m> </p></li>
<li><p> <m>\pi</m> </p></li>
<li><p> <m>\frac{3\pi}{4}</m> </p></li>
<li><p> <m>\frac{\pi}{2}</m> </p></li>
</ol> </p>
</statement>
<answer>
<p>
B
</p>
</answer>
</task>
<task>
<statement>
<p> <m>45^{\circ}</m>
<ol marker="A." cols="2">
<li><p> <m>\frac{\pi}{4}</m> </p></li>
<li><p> <m>\pi</m> </p></li>
<li><p> <m>\frac{3\pi}{4}</m> </p></li>
<li><p> <m>\frac{\pi}{2}</m> </p></li>
</ol> </p>
</statement>
<answer>
<p>
A
</p>
</answer>
</task>
</activity>

<activity>
<introduction>
<p>
Using the fact that one turn around the circle is <m>360^{\circ}</m> and also <m>2\pi</m> radians. Find the measure of the following angles in degrees.
</p>
</introduction>
<task>
<statement>
<p> <m>\frac{\pi}{2}</m>
<ol marker="A." cols="2">
<li><p> <m>45^{\circ}</m> </p></li>
<li><p> <m>90^{\circ}</m> </p></li>
<li><p> <m>180^{\circ}</m> </p></li>
<li><p> <m>360^{\circ}</m> </p></li>
</ol> </p>
</statement>
<answer>
<p>
B
</p>
</answer>
</task>
<task>
<statement>
<p> <m>\frac{3\pi}{4}</m>
<ol marker="A." cols="2">
<li><p> <m>45^{\circ}</m> </p></li>
<li><p> <m>90^{\circ}</m> </p></li>
<li><p> <m>135^{\circ}</m> </p></li>
<li><p> <m>180^{\circ}</m> </p></li>
</ol> </p>
</statement>
<answer>
<p>
C
</p>
</answer>
</task>
</activity>
</subsection>

<exercises>
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