Skip to content

Precalculus PF Accessibility #921

New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Merged
jkostiuk merged 19 commits into from
Feb 10, 2026
Merged

Precalculus PF Accessibility #921

Show file tree
Hide file tree
Changes from all commits
Commits
Show all changes
19 commits
Select commit Hold shift + click to select a range
9a02ca0
Merge precalculus-prefigure
siwelwerd Jan 27, 2026
8618289
PF1 images
siwelwerd Jan 27, 2026
b4b4028
Filename typo
siwelwerd Jan 27, 2026
0a7eaa6
Remove old file
siwelwerd Jan 27, 2026
16283e7
PF2 graphs
siwelwerd Jan 27, 2026
1badf8d
Rename file
siwelwerd Jan 27, 2026
e449c0e
PF3 graphs
siwelwerd Jan 27, 2026
97779b0
PF3 graphs
siwelwerd Jan 27, 2026
90c5772
Missing namespace
siwelwerd Jan 27, 2026
9a1e6db
Fix labels
siwelwerd Jan 27, 2026
709ad4b
Fix some annotations
siwelwerd Jan 28, 2026
50abf63
Use new trig functions for better code readability
siwelwerd Jan 28, 2026
86c7192
Typo
siwelwerd Feb 9, 2026
99ecc3c
Typo
siwelwerd Feb 9, 2026
f924c15
More typos
siwelwerd Feb 9, 2026
8cfb2ea
Fix hint
siwelwerd Feb 9, 2026
2b38b6b
Change -pi to negative pi so negative gets read out
siwelwerd Feb 9, 2026
659343b
Merge branch 'main' into precalculus-PF-accessibility
siwelwerd Feb 9, 2026
be06530
Add annotations
siwelwerd Feb 10, 2026
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
317 changes: 131 additions & 186 deletions source/precalculus/source/07-PF/01.ptx
View file
Open in desktop

Large diffs are not rendered by default.

244 changes: 97 additions & 147 deletions source/precalculus/source/07-PF/02.ptx
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -245,19 +245,11 @@
</statement>
<answer>
<p>
<image>
<sageplot>
<xi:include parse="text" href="../../../common/sagemath/library.sage"/>
P=TBIL.trig_plot(tan(x),(x,0,2*pi),ymin=-pi,ymax=pi,ticks=[pi/6,1],aspect_ratio=1,gridlines=True,detect_poles=True)
#Be sure to skip (2k+1)pi/2
xvals=[pi*i/6 for i in [0..12] if (i-3) % 6 != 0] + [pi*i/4 for i in [0..8] if (i-2) % 4 != 0]
for xval in xvals:
P+=point((xval,tan(xval)),pointsize=50,color='blue')
P+=line([(pi/2,-pi),(pi/2,pi)],color="red", linestyle="dashed",thickness=2)
P+=line([(3*pi/2,-pi),(3*pi/2,pi)],color="red", linestyle="dashed",thickness=2)
P
</sageplot>
</image>
<image>
<prefigure xmlns="https://prefigure.org" label="prefigure-PF2-graph-tan-points">
<xi:include href="prefigure/PF2-graph-tan-points.xml"/>
</prefigure>
</image>
</p>
</answer>
</task>
Expand Down Expand Up @@ -543,19 +535,11 @@ P
</statement>
<answer>
<p>
<image>
<sageplot>
<xi:include parse="text" href="../../../common/sagemath/library.sage"/>
P=TBIL.trig_plot(sec(x),(x,0,2*pi),ymin=-pi,ymax=pi,ticks=[pi/6,1],aspect_ratio=1,gridlines=True,detect_poles=True)
#Be sure to skip (2k+1)pi/2
xvals=[pi*i/6 for i in [0..12] if (i-3) % 6 != 0] + [pi*i/4 for i in [0..8] if (i-2) % 4 != 0]
for xval in xvals:
P+=point((xval,sec(xval)),pointsize=50,color='blue')
P+=line([(pi/2,-pi),(pi/2,pi)],color="red", linestyle="dashed",thickness=2)
P+=line([(3*pi/2,-pi),(3*pi/2,pi)],color="red", linestyle="dashed",thickness=2)
P
</sageplot>
</image>
<image>
<prefigure xmlns="https://prefigure.org" label="prefigure-PF2-graph-sec-points">
<xi:include href="prefigure/PF2-graph-sec-points.xml"/>
</prefigure>
</image>
</p>
</answer>
</task>
Expand Down Expand Up @@ -619,17 +603,14 @@ P
for every point <m>(a,b)</m> on the graph of <m>\cos(x)</m>, the point <m>(a,\frac{1}{b})</m>
is on the graph of <m>\sec(x)</m>.
</p>
<figure xml:id="graph-sec-PF3">
<caption><m>y=\sec(x)</m></caption>
<image><sageplot>
<xi:include parse="text" href="../../../common/sagemath/library.sage"/>
p=TBIL.trig_plot(sec(x),(x,-2*pi,2*pi),ymin=-2*pi,ymax=2*pi,ticks=[pi/2,1],aspect_ratio=1,gridlines=True,detect_poles=True)
p+=TBIL.trig_plot(cos(x),(x,-2*pi,2*pi),ymin=-2*pi,ymax=2*pi,ticks=[pi/2,1],aspect_ratio=1,gridlines=True,detect_poles=True,color="green",linestyle="dotted")
for i in [-2..1]:
p+=line([(i*pi+pi/2,-2*pi),(i*pi+pi/2,2*pi)],thickness=3,linestyle='dashed',color='red')
p
</sageplot></image>
</figure>
<figure xml:id="graph-sec-PF3">
<caption><m>y=\sec(x)</m></caption>
<image>
<prefigure xmlns="https://prefigure.org" label="prefigure-PF2-graph-sec-cos">
<xi:include href="prefigure/PF2-graph-sec-cos.xml"/>
</prefigure>
</image>
</figure>
</observation>


Expand All @@ -649,11 +630,10 @@ p
<hint>
<p>Recall the graph of <m>\sin(x)</m></p>
<figure>
<image width="50%">
<sageplot>
<xi:include parse="text" href="../../../common/sagemath/library.sage"/>
P=TBIL.trig_plot(sin(x),(x,-2*pi,2*pi),ymin=-pi,ymax=pi,ticks=[pi/4,1],aspect_ratio=1,gridlines=True,detect_poles=True)
</sageplot>
<image>
<prefigure xmlns="https://prefigure.org" label="prefigure-PF2-sine">
<xi:include href="prefigure/PF1-sine.xml"/>
</prefigure>
</image>
</figure>
</hint>
Expand Down Expand Up @@ -716,15 +696,10 @@ P=TBIL.trig_plot(sin(x),(x,-2*pi,2*pi),ymin=-pi,ymax=pi,ticks=[pi/4,1],aspect_ra
<answer>
<p>
<image>
<sageplot>
<xi:include parse="text" href="../../../common/sagemath/library.sage"/>
P=TBIL.trig_plot(csc(x),(x,0,2*pi),ymin=-pi,ymax=pi,ticks=[pi/6,1],aspect_ratio=1,gridlines=True,detect_poles=True)
P+=line([(0,-pi),(0,pi)],color="red", linestyle="dashed",thickness=2)
P+=line([(pi,-pi),(pi,pi)],color="red", linestyle="dashed",thickness=2)
P+=line([(2*pi,-pi),(2*pi,pi)],color="red", linestyle="dashed",thickness=2)
P
</sageplot>
</image>
<prefigure xmlns="https://prefigure.org" label="prefigure-PF2-graph-csc">
<xi:include href="prefigure/PF2-graph-csc.xml"/>
</prefigure>
</image>
</p>
</answer>
</task>
Expand Down Expand Up @@ -788,17 +763,14 @@ P
for every point <m>(a,b)</m> on the graph of <m>\sin(x)</m>, the point <m>(a,\frac{1}{b})</m>
is on the graph of <m>\csc(x)</m>.
</p>
<figure xml:id="graph-csc-PF3">
<caption><m>y=\csc(x)</m></caption>
<image><sageplot>
<xi:include parse="text" href="../../../common/sagemath/library.sage"/>
p=TBIL.trig_plot(csc(x),(x,-2*pi,2*pi),ymin=-2*pi,ymax=2*pi,ticks=[pi/2,1],aspect_ratio=1,gridlines=True,detect_poles=True)
p+=TBIL.trig_plot(sin(x),(x,-2*pi,2*pi),ymin=-2*pi,ymax=2*pi,ticks=[pi/2,1],aspect_ratio=1,gridlines=True,detect_poles=True,color="green",linestyle="dotted")
for i in [-2..2]:
p+=line([(i*pi,-2*pi),(i*pi,2*pi)],thickness=3,linestyle='dashed',color='red')
p
</sageplot></image>
</figure>
<figure xml:id="graph-csc-PF3">
<caption><m>y=\csc(x)</m></caption>
<image>
<prefigure xmlns="https://prefigure.org" label="prefigure-PF2-graph-csc-sin">
<xi:include href="prefigure/PF2-graph-csc-sin.xml"/>
</prefigure>
</image>
</figure>
</observation>

<activity xml:id="activity-cot-table">
Expand All @@ -813,17 +785,7 @@ p
</statement>
<hint>
<p>Recall the graph of <m>\tan(x)</m></p>
<figure>
<image width="50%">
<sageplot>
<xi:include parse="text" href="../../../common/sagemath/library.sage"/>
P=TBIL.trig_plot(tan(x),(x,-2*pi,2*pi),ymin=-pi,ymax=pi,ticks=[pi/4,1],aspect_ratio=1,gridlines=True,detect_poles=True)
for i in [-2..1]:
P+=line([(i*pi+pi/2,-2*pi),(i*pi+pi/2,2*pi)],thickness=3,linestyle='dashed',color='red')
P
</sageplot>
</image>
</figure>
<xref ref="graph-tan"/>
</hint>
<answer>
<p><m>\ldots,-2\pi,-\pi,0,\pi,2\pi,\ldots</m></p>
Expand Down Expand Up @@ -885,16 +847,11 @@ P
<hint><p>It may be helpful to first sketch the graph of <m>\tan(x)</m>.</p></hint>
<answer>
<p>
<image>
<sageplot>
<xi:include parse="text" href="../../../common/sagemath/library.sage"/>
P=TBIL.trig_plot(cot(x),(x,0,2*pi),ymin=-pi,ymax=pi,ticks=[pi/4,1],aspect_ratio=1,gridlines=True,detect_poles=True)
P+=line([(0,-pi),(0,pi)],color="red", linestyle="dashed",thickness=2)
P+=line([(pi,-pi),(pi,pi)],color="red", linestyle="dashed",thickness=2)
P+=line([(2*pi,-pi),(2*pi,pi)],color="red", linestyle="dashed",thickness=2)
P
</sageplot>
</image>
<image>
<prefigure xmlns="https://prefigure.org" label="prefigure-PF2-graph-cot">
<xi:include href="prefigure/PF2-graph-cot.xml"/>
</prefigure>
</image>
</p>
</answer>
</task>
Expand Down Expand Up @@ -958,28 +915,24 @@ P
for every point <m>(a,b)</m> on the graph of <m>\tan(x)</m>, the point <m>(a,\frac{1}{b})</m>
is on the graph of <m>\cot(x)</m>.
</p>
<sidebyside>
<figure xml:id="graph-tan-PF3">
<caption><m>y=\tan(x)</m></caption>
<image><sageplot>
<xi:include parse="text" href="../../../common/sagemath/library.sage"/>
p=TBIL.trig_plot(tan(x),(x,-2*pi,2*pi),ymin=-2*pi,ymax=2*pi,ticks=[pi/2,1],aspect_ratio=1,gridlines=True,detect_poles=True)
for i in [-2..1]:
p+=line([(i*pi+pi/2,-2*pi),(i*pi+pi/2,2*pi)],thickness=3,linestyle='dashed',color='red')
p
</sageplot></image>
</figure>
<figure xml:id="graph-cot-PF3">
<caption><m>y=\cot(x)</m></caption>
<image><sageplot>
<xi:include parse="text" href="../../../common/sagemath/library.sage"/>
p=TBIL.trig_plot(cot(x),(x,-2*pi,2*pi),ymin=-2*pi,ymax=2*pi,ticks=[pi/2,1],aspect_ratio=1,gridlines=True,detect_poles=True)
for i in [-2..2]:
p+=line([(i*pi,-2*pi),(i*pi,2*pi)],thickness=3,linestyle='dashed',color='red')
p
</sageplot></image>
</figure>
</sidebyside>
<sidebyside>
<figure xml:id="graph-tan-PF3">
<caption><m>y=\tan(x)</m></caption>
<image>
<prefigure xmlns="https://prefigure.org" label="prefigure-PF2-graph-tan2">
<xi:include href="prefigure/PF2-graph-tan2.xml"/>
</prefigure>
</image>
</figure>
<figure xml:id="graph-cot-PF3">
<caption><m>y=\cot(x)</m></caption>
<image>
<prefigure xmlns="https://prefigure.org" label="prefigure-PF2-graph-cot2">
<xi:include href="prefigure/PF2-graph-cot2.xml"/>
</prefigure>
</image>
</figure>
</sidebyside>
</observation>

<remark>
Expand Down Expand Up @@ -1013,33 +966,34 @@ p
<statement>
<p>Which of the following is the graph of <m>g(x)=\sec\left(x+\dfrac{\pi}{2}\right)</m>?</p>
<ol marker="A." cols="2">
<li><image><sageplot>
<xi:include parse="text" href="../../../common/sagemath/library.sage"/>
p=TBIL.trig_plot(sec(x),(x,-2*pi,2*pi),ymin=-2*pi,ymax=2*pi,ticks=[pi/2,1],aspect_ratio=1,gridlines=True,detect_poles=True)
for i in [-2..1]:
p+=line([(i*pi+pi/2,-2*pi),(i*pi+pi/2,2*pi)],thickness=3,linestyle='dashed',color='red')
p
</sageplot></image></li>
<li><image><sageplot>
<xi:include parse="text" href="../../../common/sagemath/library.sage"/>
p=TBIL.trig_plot(sec(x+pi),(x,-2*pi,2*pi),ymin=-2*pi,ymax=2*pi,ticks=[pi/2,1],aspect_ratio=1,gridlines=True,detect_poles=True)
for i in [-2..1]:
p+=line([(i*pi+pi/2,-2*pi),(i*pi+pi/2,2*pi)],thickness=3,linestyle='dashed',color='red')
p
</sageplot></image></li>
<li><image><sageplot>
<xi:include parse="text" href="../../../common/sagemath/library.sage"/>
p=TBIL.trig_plot(sec(x-pi/2),(x,-2*pi,2*pi),ymin=-2*pi,ymax=2*pi,ticks=[pi/2,1],aspect_ratio=1,gridlines=True,detect_poles=True)
for i in [-2..2]:
p+=line([(i*pi,-2*pi),(i*pi,2*pi)],thickness=3,linestyle='dashed',color='red')
p
</sageplot></image></li> <li><image><sageplot>
<xi:include parse="text" href="../../../common/sagemath/library.sage"/>
p=TBIL.trig_plot(sec(x+pi/2),(x,-2*pi,2*pi),ymin=-2*pi,ymax=2*pi,ticks=[pi/2,1],aspect_ratio=1,gridlines=True,detect_poles=True)
for i in [-2..2]:
p+=line([(i*pi,-2*pi),(i*pi,2*pi)],thickness=3,linestyle='dashed',color='red')
p
</sageplot></image></li>
<li>
<image>
<prefigure xmlns="https://prefigure.org" label="prefigure-PF2-graph-sec-transform1">
<xi:include href="prefigure/PF2-sec-transform1.xml"/>
</prefigure>
</image>
</li>
<li>
<image>
<prefigure xmlns="https://prefigure.org" label="prefigure-PF2-graph-sec-transform2">
<xi:include href="prefigure/PF2-sec-transform2.xml"/>
</prefigure>
</image>
</li>
<li>
<image>
<prefigure xmlns="https://prefigure.org" label="prefigure-PF2-graph-sec-transform3">
<xi:include href="prefigure/PF2-sec-transform3.xml"/>
</prefigure>
</image>
</li>
<li>
<image>
<prefigure xmlns="https://prefigure.org" label="prefigure-PF2-graph-sec-transform4">
<xi:include href="prefigure/PF2-sec-transform4.xml"/>
</prefigure>
</image>
</li>
</ol>
</statement>
<answer>
Expand Down Expand Up @@ -1129,7 +1083,7 @@ p
<li><m>\ldots,-\dfrac{\pi}{4},0,\dfrac{\pi}{4},,\ldots</m></li>
</ol>
</statement>
<hint><p>Recall that <m>\tan(x)</m> has zeroes asymptotes at <m>\pi k</m> for each integer <m>k</m>.</p></hint>
<hint><p>Recall that <m>\tan(x)</m> has zeroes at <m>\pi k</m> for each integer <m>k</m>.</p></hint>
<answer>
<p>C.</p>
</answer>
Expand All @@ -1139,13 +1093,11 @@ p
<p>Graph <m>h(x)=\tan(2x)</m>.</p>
</statement>
<answer>
<image><sageplot>
<xi:include parse="text" href="../../../common/sagemath/library.sage"/>
p=TBIL.trig_plot(tan(2*x),(x,-2*pi,2*pi),ymin=-2*pi,ymax=2*pi,ticks=[pi/2,1],aspect_ratio=1,gridlines=True,detect_poles=True,thickness=2)
for i in [-4..3]:
p+=line([(i*pi/2+pi/4,-2*pi),(i*pi/2+pi/4,2*pi)],thickness=2,linestyle='dashed',color='red')
p
</sageplot></image>
<image>
<prefigure xmlns="https://prefigure.org" label="prefigure-PF2-graph-tan2x">
<xi:include href="prefigure/PF2-tan2x.xml"/>
</prefigure>
</image>
</answer>
</task>
<task>
Expand Down Expand Up @@ -1209,13 +1161,11 @@ p
<p>Graph <m>k(x)=3\csc\left(\dfrac{x}{2}\right)</m>.</p>
</statement>
<answer>
<image><sageplot>
<xi:include parse="text" href="../../../common/sagemath/library.sage"/>
p=TBIL.trig_plot(3*csc(x/2),(x,-4*pi,4*pi),ymin=-2*pi,ymax=2*pi,ticks=[pi/2,1],aspect_ratio=1,gridlines=True,detect_poles=True,thickness=2)
for i in [-2..2]:
p+=line([(i*2*pi,-2*pi),(i*2*pi,2*pi)],thickness=2,linestyle='dashed',color='red')
p
</sageplot></image>
<image>
<prefigure xmlns="https://prefigure.org" label="prefigure-PF2-graph-fluency">
<xi:include href="prefigure/PF2-graph-fluency.xml"/>
</prefigure>
</image>
</answer>
</task>
<task>
Expand Down
Loading