Skip to content

Commit 74f741e

Browse files
siwelwerdsiwelwerd
authored
Precalculus PF Accessibility (#921)
* Merge precalculus-prefigure * PF1 images * Filename typo * Remove old file * PF2 graphs * Rename file * PF3 graphs * PF3 graphs * Missing namespace * Fix labels * Fix some annotations * Use new trig functions for better code readability * Typo * Typo * More typos * Fix hint * Change -pi to negative pi so negative gets read out * Add annotations
1 parent 1004ec9 commit 74f741e

56 files changed

Lines changed: 1151 additions & 428 deletions

Some content is hidden

Large Commits have some content hidden by default. Use the searchbox below for content that may be hidden.

‎source/precalculus/source/07-PF/01.ptx‎

Lines changed: 131 additions & 186 deletions
Large diffs are not rendered by default.

‎source/precalculus/source/07-PF/02.ptx‎

Lines changed: 97 additions & 147 deletions
Original file line numberDiff line numberDiff line change
@@ -245,19 +245,11 @@
245245
</statement>
246246
<answer>
247247
<p>
248-
<image>
249-
<sageplot>
250-
<xi:include parse="text" href="../../../common/sagemath/library.sage"/>
251-
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)
252-
#Be sure to skip (2k+1)pi/2
253-
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]
254-
for xval in xvals:
255-
P+=point((xval,tan(xval)),pointsize=50,color='blue')
256-
P+=line([(pi/2,-pi),(pi/2,pi)],color="red", linestyle="dashed",thickness=2)
257-
P+=line([(3*pi/2,-pi),(3*pi/2,pi)],color="red", linestyle="dashed",thickness=2)
258-
P
259-
</sageplot>
260-
</image>
248+
<image>
249+
<prefigure xmlns="https://prefigure.org" label="prefigure-PF2-graph-tan-points">
250+
<xi:include href="prefigure/PF2-graph-tan-points.xml"/>
251+
</prefigure>
252+
</image>
261253
</p>
262254
</answer>
263255
</task>
@@ -543,19 +535,11 @@ P
543535
</statement>
544536
<answer>
545537
<p>
546-
<image>
547-
<sageplot>
548-
<xi:include parse="text" href="../../../common/sagemath/library.sage"/>
549-
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)
550-
#Be sure to skip (2k+1)pi/2
551-
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]
552-
for xval in xvals:
553-
P+=point((xval,sec(xval)),pointsize=50,color='blue')
554-
P+=line([(pi/2,-pi),(pi/2,pi)],color="red", linestyle="dashed",thickness=2)
555-
P+=line([(3*pi/2,-pi),(3*pi/2,pi)],color="red", linestyle="dashed",thickness=2)
556-
P
557-
</sageplot>
558-
</image>
538+
<image>
539+
<prefigure xmlns="https://prefigure.org" label="prefigure-PF2-graph-sec-points">
540+
<xi:include href="prefigure/PF2-graph-sec-points.xml"/>
541+
</prefigure>
542+
</image>
559543
</p>
560544
</answer>
561545
</task>
@@ -619,17 +603,14 @@ P
619603
for every point <m>(a,b)</m> on the graph of <m>\cos(x)</m>, the point <m>(a,\frac{1}{b})</m>
620604
is on the graph of <m>\sec(x)</m>.
621605
</p>
622-
<figure xml:id="graph-sec-PF3">
623-
<caption><m>y=\sec(x)</m></caption>
624-
<image><sageplot>
625-
<xi:include parse="text" href="../../../common/sagemath/library.sage"/>
626-
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)
627-
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")
628-
for i in [-2..1]:
629-
p+=line([(i*pi+pi/2,-2*pi),(i*pi+pi/2,2*pi)],thickness=3,linestyle='dashed',color='red')
630-
p
631-
</sageplot></image>
632-
</figure>
606+
<figure xml:id="graph-sec-PF3">
607+
<caption><m>y=\sec(x)</m></caption>
608+
<image>
609+
<prefigure xmlns="https://prefigure.org" label="prefigure-PF2-graph-sec-cos">
610+
<xi:include href="prefigure/PF2-graph-sec-cos.xml"/>
611+
</prefigure>
612+
</image>
613+
</figure>
633614
</observation>
634615

635616

@@ -649,11 +630,10 @@ p
649630
<hint>
650631
<p>Recall the graph of <m>\sin(x)</m></p>
651632
<figure>
652-
<image width="50%">
653-
<sageplot>
654-
<xi:include parse="text" href="../../../common/sagemath/library.sage"/>
655-
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)
656-
</sageplot>
633+
<image>
634+
<prefigure xmlns="https://prefigure.org" label="prefigure-PF2-sine">
635+
<xi:include href="prefigure/PF1-sine.xml"/>
636+
</prefigure>
657637
</image>
658638
</figure>
659639
</hint>
@@ -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
716696
<answer>
717697
<p>
718698
<image>
719-
<sageplot>
720-
<xi:include parse="text" href="../../../common/sagemath/library.sage"/>
721-
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)
722-
P+=line([(0,-pi),(0,pi)],color="red", linestyle="dashed",thickness=2)
723-
P+=line([(pi,-pi),(pi,pi)],color="red", linestyle="dashed",thickness=2)
724-
P+=line([(2*pi,-pi),(2*pi,pi)],color="red", linestyle="dashed",thickness=2)
725-
P
726-
</sageplot>
727-
</image>
699+
<prefigure xmlns="https://prefigure.org" label="prefigure-PF2-graph-csc">
700+
<xi:include href="prefigure/PF2-graph-csc.xml"/>
701+
</prefigure>
702+
</image>
728703
</p>
729704
</answer>
730705
</task>
@@ -788,17 +763,14 @@ P
788763
for every point <m>(a,b)</m> on the graph of <m>\sin(x)</m>, the point <m>(a,\frac{1}{b})</m>
789764
is on the graph of <m>\csc(x)</m>.
790765
</p>
791-
<figure xml:id="graph-csc-PF3">
792-
<caption><m>y=\csc(x)</m></caption>
793-
<image><sageplot>
794-
<xi:include parse="text" href="../../../common/sagemath/library.sage"/>
795-
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)
796-
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")
797-
for i in [-2..2]:
798-
p+=line([(i*pi,-2*pi),(i*pi,2*pi)],thickness=3,linestyle='dashed',color='red')
799-
p
800-
</sageplot></image>
801-
</figure>
766+
<figure xml:id="graph-csc-PF3">
767+
<caption><m>y=\csc(x)</m></caption>
768+
<image>
769+
<prefigure xmlns="https://prefigure.org" label="prefigure-PF2-graph-csc-sin">
770+
<xi:include href="prefigure/PF2-graph-csc-sin.xml"/>
771+
</prefigure>
772+
</image>
773+
</figure>
802774
</observation>
803775

804776
<activity xml:id="activity-cot-table">
@@ -813,17 +785,7 @@ p
813785
</statement>
814786
<hint>
815787
<p>Recall the graph of <m>\tan(x)</m></p>
816-
<figure>
817-
<image width="50%">
818-
<sageplot>
819-
<xi:include parse="text" href="../../../common/sagemath/library.sage"/>
820-
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)
821-
for i in [-2..1]:
822-
P+=line([(i*pi+pi/2,-2*pi),(i*pi+pi/2,2*pi)],thickness=3,linestyle='dashed',color='red')
823-
P
824-
</sageplot>
825-
</image>
826-
</figure>
788+
<xref ref="graph-tan"/>
827789
</hint>
828790
<answer>
829791
<p><m>\ldots,-2\pi,-\pi,0,\pi,2\pi,\ldots</m></p>
@@ -885,16 +847,11 @@ P
885847
<hint><p>It may be helpful to first sketch the graph of <m>\tan(x)</m>.</p></hint>
886848
<answer>
887849
<p>
888-
<image>
889-
<sageplot>
890-
<xi:include parse="text" href="../../../common/sagemath/library.sage"/>
891-
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)
892-
P+=line([(0,-pi),(0,pi)],color="red", linestyle="dashed",thickness=2)
893-
P+=line([(pi,-pi),(pi,pi)],color="red", linestyle="dashed",thickness=2)
894-
P+=line([(2*pi,-pi),(2*pi,pi)],color="red", linestyle="dashed",thickness=2)
895-
P
896-
</sageplot>
897-
</image>
850+
<image>
851+
<prefigure xmlns="https://prefigure.org" label="prefigure-PF2-graph-cot">
852+
<xi:include href="prefigure/PF2-graph-cot.xml"/>
853+
</prefigure>
854+
</image>
898855
</p>
899856
</answer>
900857
</task>
@@ -958,28 +915,24 @@ P
958915
for every point <m>(a,b)</m> on the graph of <m>\tan(x)</m>, the point <m>(a,\frac{1}{b})</m>
959916
is on the graph of <m>\cot(x)</m>.
960917
</p>
961-
<sidebyside>
962-
<figure xml:id="graph-tan-PF3">
963-
<caption><m>y=\tan(x)</m></caption>
964-
<image><sageplot>
965-
<xi:include parse="text" href="../../../common/sagemath/library.sage"/>
966-
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)
967-
for i in [-2..1]:
968-
p+=line([(i*pi+pi/2,-2*pi),(i*pi+pi/2,2*pi)],thickness=3,linestyle='dashed',color='red')
969-
p
970-
</sageplot></image>
971-
</figure>
972-
<figure xml:id="graph-cot-PF3">
973-
<caption><m>y=\cot(x)</m></caption>
974-
<image><sageplot>
975-
<xi:include parse="text" href="../../../common/sagemath/library.sage"/>
976-
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)
977-
for i in [-2..2]:
978-
p+=line([(i*pi,-2*pi),(i*pi,2*pi)],thickness=3,linestyle='dashed',color='red')
979-
p
980-
</sageplot></image>
981-
</figure>
982-
</sidebyside>
918+
<sidebyside>
919+
<figure xml:id="graph-tan-PF3">
920+
<caption><m>y=\tan(x)</m></caption>
921+
<image>
922+
<prefigure xmlns="https://prefigure.org" label="prefigure-PF2-graph-tan2">
923+
<xi:include href="prefigure/PF2-graph-tan2.xml"/>
924+
</prefigure>
925+
</image>
926+
</figure>
927+
<figure xml:id="graph-cot-PF3">
928+
<caption><m>y=\cot(x)</m></caption>
929+
<image>
930+
<prefigure xmlns="https://prefigure.org" label="prefigure-PF2-graph-cot2">
931+
<xi:include href="prefigure/PF2-graph-cot2.xml"/>
932+
</prefigure>
933+
</image>
934+
</figure>
935+
</sidebyside>
983936
</observation>
984937

985938
<remark>
@@ -1013,33 +966,34 @@ p
1013966
<statement>
1014967
<p>Which of the following is the graph of <m>g(x)=\sec\left(x+\dfrac{\pi}{2}\right)</m>?</p>
1015968
<ol marker="A." cols="2">
1016-
<li><image><sageplot>
1017-
<xi:include parse="text" href="../../../common/sagemath/library.sage"/>
1018-
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)
1019-
for i in [-2..1]:
1020-
p+=line([(i*pi+pi/2,-2*pi),(i*pi+pi/2,2*pi)],thickness=3,linestyle='dashed',color='red')
1021-
p
1022-
</sageplot></image></li>
1023-
<li><image><sageplot>
1024-
<xi:include parse="text" href="../../../common/sagemath/library.sage"/>
1025-
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)
1026-
for i in [-2..1]:
1027-
p+=line([(i*pi+pi/2,-2*pi),(i*pi+pi/2,2*pi)],thickness=3,linestyle='dashed',color='red')
1028-
p
1029-
</sageplot></image></li>
1030-
<li><image><sageplot>
1031-
<xi:include parse="text" href="../../../common/sagemath/library.sage"/>
1032-
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)
1033-
for i in [-2..2]:
1034-
p+=line([(i*pi,-2*pi),(i*pi,2*pi)],thickness=3,linestyle='dashed',color='red')
1035-
p
1036-
</sageplot></image></li> <li><image><sageplot>
1037-
<xi:include parse="text" href="../../../common/sagemath/library.sage"/>
1038-
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)
1039-
for i in [-2..2]:
1040-
p+=line([(i*pi,-2*pi),(i*pi,2*pi)],thickness=3,linestyle='dashed',color='red')
1041-
p
1042-
</sageplot></image></li>
969+
<li>
970+
<image>
971+
<prefigure xmlns="https://prefigure.org" label="prefigure-PF2-graph-sec-transform1">
972+
<xi:include href="prefigure/PF2-sec-transform1.xml"/>
973+
</prefigure>
974+
</image>
975+
</li>
976+
<li>
977+
<image>
978+
<prefigure xmlns="https://prefigure.org" label="prefigure-PF2-graph-sec-transform2">
979+
<xi:include href="prefigure/PF2-sec-transform2.xml"/>
980+
</prefigure>
981+
</image>
982+
</li>
983+
<li>
984+
<image>
985+
<prefigure xmlns="https://prefigure.org" label="prefigure-PF2-graph-sec-transform3">
986+
<xi:include href="prefigure/PF2-sec-transform3.xml"/>
987+
</prefigure>
988+
</image>
989+
</li>
990+
<li>
991+
<image>
992+
<prefigure xmlns="https://prefigure.org" label="prefigure-PF2-graph-sec-transform4">
993+
<xi:include href="prefigure/PF2-sec-transform4.xml"/>
994+
</prefigure>
995+
</image>
996+
</li>
1043997
</ol>
1044998
</statement>
1045999
<answer>
@@ -1129,7 +1083,7 @@ p
11291083
<li><m>\ldots,-\dfrac{\pi}{4},0,\dfrac{\pi}{4},,\ldots</m></li>
11301084
</ol>
11311085
</statement>
1132-
<hint><p>Recall that <m>\tan(x)</m> has zeroes asymptotes at <m>\pi k</m> for each integer <m>k</m>.</p></hint>
1086+
<hint><p>Recall that <m>\tan(x)</m> has zeroes at <m>\pi k</m> for each integer <m>k</m>.</p></hint>
11331087
<answer>
11341088
<p>C.</p>
11351089
</answer>
@@ -1139,13 +1093,11 @@ p
11391093
<p>Graph <m>h(x)=\tan(2x)</m>.</p>
11401094
</statement>
11411095
<answer>
1142-
<image><sageplot>
1143-
<xi:include parse="text" href="../../../common/sagemath/library.sage"/>
1144-
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)
1145-
for i in [-4..3]:
1146-
p+=line([(i*pi/2+pi/4,-2*pi),(i*pi/2+pi/4,2*pi)],thickness=2,linestyle='dashed',color='red')
1147-
p
1148-
</sageplot></image>
1096+
<image>
1097+
<prefigure xmlns="https://prefigure.org" label="prefigure-PF2-graph-tan2x">
1098+
<xi:include href="prefigure/PF2-tan2x.xml"/>
1099+
</prefigure>
1100+
</image>
11491101
</answer>
11501102
</task>
11511103
<task>
@@ -1209,13 +1161,11 @@ p
12091161
<p>Graph <m>k(x)=3\csc\left(\dfrac{x}{2}\right)</m>.</p>
12101162
</statement>
12111163
<answer>
1212-
<image><sageplot>
1213-
<xi:include parse="text" href="../../../common/sagemath/library.sage"/>
1214-
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)
1215-
for i in [-2..2]:
1216-
p+=line([(i*2*pi,-2*pi),(i*2*pi,2*pi)],thickness=2,linestyle='dashed',color='red')
1217-
p
1218-
</sageplot></image>
1164+
<image>
1165+
<prefigure xmlns="https://prefigure.org" label="prefigure-PF2-graph-fluency">
1166+
<xi:include href="prefigure/PF2-graph-fluency.xml"/>
1167+
</prefigure>
1168+
</image>
12191169
</answer>
12201170
</task>
12211171
<task>

0 commit comments

Comments
 (0)