From 9a02ca0c5a4960bb1e3afad9a668d39e9d5e69e4 Mon Sep 17 00:00:00 2001 From: Drew Lewis Date: Tue, 27 Jan 2026 00:29:40 +0000 Subject: [PATCH 01/12] Merge precalculus-prefigure --- requirements.txt | 2 +- source/precalculus/source/meta/graphs.ptx | 269 +++++++++--------- .../source/meta/prefigure/graph-absolute.xml | 12 + .../source/meta/prefigure/graph-arccos.xml | 12 + .../source/meta/prefigure/graph-arccot.xml | 19 ++ .../source/meta/prefigure/graph-arccsc.xml | 16 ++ .../source/meta/prefigure/graph-arcsec.xml | 16 ++ .../source/meta/prefigure/graph-arcsin.xml | 12 + .../source/meta/prefigure/graph-arctan.xml | 18 ++ .../source/meta/prefigure/graph-cos.xml | 12 + .../source/meta/prefigure/graph-cot.xml | 24 ++ .../source/meta/prefigure/graph-csc.xml | 24 ++ .../meta/prefigure/graph-exponential.xml | 16 ++ .../meta/prefigure/graph-exponentiale.xml | 16 ++ .../prefigure/graph-logarithm-natural.xml | 16 ++ .../source/meta/prefigure/graph-logarithm.xml | 16 ++ .../source/meta/prefigure/graph-sec.xml | 22 ++ .../source/meta/prefigure/graph-sin.xml | 12 + .../meta/prefigure/graph-square-root.xml | 12 + .../source/meta/prefigure/graph-tan.xml | 22 ++ .../source/meta/prefigure/graphx-minus1.xml | 18 ++ .../source/meta/prefigure/graphx-minus2.xml | 18 ++ .../source/meta/prefigure/graphx-minus3.xml | 18 ++ .../source/meta/prefigure/graphx-minus4.xml | 18 ++ .../source/meta/prefigure/graphx.xml | 12 + .../source/meta/prefigure/graphx2.xml | 12 + .../source/meta/prefigure/graphx3.xml | 12 + .../source/meta/prefigure/graphx4.xml | 12 + 28 files changed, 548 insertions(+), 140 deletions(-) create mode 100644 source/precalculus/source/meta/prefigure/graph-absolute.xml create mode 100644 source/precalculus/source/meta/prefigure/graph-arccos.xml create mode 100644 source/precalculus/source/meta/prefigure/graph-arccot.xml create mode 100644 source/precalculus/source/meta/prefigure/graph-arccsc.xml create mode 100644 source/precalculus/source/meta/prefigure/graph-arcsec.xml create mode 100644 source/precalculus/source/meta/prefigure/graph-arcsin.xml create mode 100644 source/precalculus/source/meta/prefigure/graph-arctan.xml create mode 100644 source/precalculus/source/meta/prefigure/graph-cos.xml create mode 100644 source/precalculus/source/meta/prefigure/graph-cot.xml create mode 100644 source/precalculus/source/meta/prefigure/graph-csc.xml create mode 100644 source/precalculus/source/meta/prefigure/graph-exponential.xml create mode 100644 source/precalculus/source/meta/prefigure/graph-exponentiale.xml create mode 100644 source/precalculus/source/meta/prefigure/graph-logarithm-natural.xml create mode 100644 source/precalculus/source/meta/prefigure/graph-logarithm.xml create mode 100644 source/precalculus/source/meta/prefigure/graph-sec.xml create mode 100644 source/precalculus/source/meta/prefigure/graph-sin.xml create mode 100644 source/precalculus/source/meta/prefigure/graph-square-root.xml create mode 100644 source/precalculus/source/meta/prefigure/graph-tan.xml create mode 100644 source/precalculus/source/meta/prefigure/graphx-minus1.xml create mode 100644 source/precalculus/source/meta/prefigure/graphx-minus2.xml create mode 100644 source/precalculus/source/meta/prefigure/graphx-minus3.xml create mode 100644 source/precalculus/source/meta/prefigure/graphx-minus4.xml create mode 100644 source/precalculus/source/meta/prefigure/graphx.xml create mode 100644 source/precalculus/source/meta/prefigure/graphx2.xml create mode 100644 source/precalculus/source/meta/prefigure/graphx3.xml create mode 100644 source/precalculus/source/meta/prefigure/graphx4.xml diff --git a/requirements.txt b/requirements.txt index 863188880..864ae915c 100644 --- a/requirements.txt +++ b/requirements.txt @@ -1,4 +1,4 @@ -pretext == 2.24.0 +pretext[prefigure] == 2.36.0 CodeChat-Server == 0.2.25 pelican == 4.11.0 markdown == 3.7.0 diff --git a/source/precalculus/source/meta/graphs.ptx b/source/precalculus/source/meta/graphs.ptx index ae1fbdfae..fa7503d3a 100644 --- a/source/precalculus/source/meta/graphs.ptx +++ b/source/precalculus/source/meta/graphs.ptx @@ -7,29 +7,37 @@
Graph of y=x - - plot(x,xmin=-5,xmax=5,ymin=-5,ymax=5,thickness=3,aspect_ratio=1,gridlines=True, ticks=[1,1]) - + + + + +
Graph of y=x^2 - - plot(x^2,xmin=-5,xmax=5,ymin=-5,ymax=5,thickness=3,aspect_ratio=1,gridlines=True, ticks=[1,1]) - + + + + +
Graph of y=x^3 - - plot(x^3,xmin=-5,xmax=5,ymin=-5,ymax=5,thickness=3,aspect_ratio=1,gridlines=True, ticks=[1,1]) - + + + + +
Graph of y=x^4 - - plot(x^4,xmin=-5,xmax=5,ymin=-5,ymax=5,thickness=3,aspect_ratio=1,gridlines=True, ticks=[1,1]) - + + + + +
@@ -40,42 +48,37 @@
Graph of y=\dfrac{1}{x} - - p=plot(1/x,xmin=-5,xmax=5,ymin=-5,ymax=5,thickness=3,aspect_ratio=1,detect_poles=True,gridlines=True, ticks=[1,1]) - p+=line([(0,-5),(0,5)],thickness=3,linestyle='dashed',color='red') - p+=line([(-5,0),(5,0)],thickness=3,linestyle='dashed',color='red') - p - + + + + +
Graph of y=\dfrac{1}{x^2} - - p=plot(1/x^2,xmin=-5,xmax=5,ymin=-5,ymax=5,thickness=3,aspect_ratio=1,detect_poles=True,gridlines=True, ticks=[1,1]) - p+=line([(0,-5),(0,5)],thickness=3,linestyle='dashed',color='red') - p+=line([(-5,0),(5,0)],thickness=3,linestyle='dashed',color='red') - p - + + + + +
Graph of y=\dfrac{1}{x^3} - - p=plot(1/x^3,xmin=-5,xmax=5,ymin=-5,ymax=5,thickness=3,aspect_ratio=1,detect_poles=True,gridlines=True, ticks=[1,1]) - p+=line([(0,-5),(0,5)],thickness=3,linestyle='dashed',color='red') - p+=line([(-5,0),(5,0)],thickness=3,linestyle='dashed',color='red') - p - + + + + +
Graph of y=\dfrac{1}{x^4} - - p=plot(1/x^4,xmin=-5,xmax=-0.1,ymin=-5,ymax=5,thickness=3,aspect_ratio=1,gridlines=True, ticks=[1,1]) - p+=plot(1/x^4,xmin=0.1,xmax=5,ymin=-5,ymax=5,thickness=3) - p+=line([(0,-5),(0,5)],thickness=3,linestyle='dashed',color='red') - p+=line([(-5,0),(5,0)],thickness=3,linestyle='dashed',color='red') - p - + + + + +
@@ -86,17 +89,19 @@
Graph of y=|x| - - plot(abs(x),xmin=-5,xmax=5,ymin=-5,ymax=5,thickness=3,aspect_ratio=1,detect_poles=True,gridlines=True, ticks=[1,1]) - + + + + +
Graph of y=\sqrt{x} - - p=plot(sqrt(x),xmin=-5,xmax=5,ymin=-5,ymax=5,thickness=3,aspect_ratio=1,detect_poles=True,gridlines=True, ticks=[1,1]) - p.SHOW_OPTIONS['xmin']=-5 - p - + + + + +
@@ -107,39 +112,37 @@
Graph of y=b^x, with b=2 - - p=plot(2^x,xmin=-5,xmax=5,ymin=-5,ymax=5,thickness=3,aspect_ratio=1,detect_poles=True,gridlines=True, ticks=[1,1]) - p+=line([(-5,0),(5,0)],thickness=3,linestyle='dashed',color='red') - p - + + + + +
Graph of y=\log_b x, with b=2 - - p=plot(log(x)/log(2),xmin=0,xmax=5,ymin=-5,ymax=5,thickness=3,aspect_ratio=1,detect_poles=True,gridlines=True, ticks=[1,1]) - p+=line([(0,-5),(0,5)],thickness=3,linestyle='dashed',color='red') - p.SHOW_OPTIONS['xmin']=-5 - p - + + + + +
Graph of y=e^x - - p=plot(e^x,xmin=-5,xmax=5,ymin=-5,ymax=5,thickness=3,aspect_ratio=1,detect_poles=True,gridlines=True, ticks=[1,1]) - p+=line([(-5,0),(5,0)],thickness=3,linestyle='dashed',color='red') - p - + + + + +
Graph of y=\ln x - - p=plot(log(x),xmin=0,xmax=5,ymin=-5,ymax=5,thickness=3,aspect_ratio=1,detect_poles=True,gridlines=True, ticks=[1,1]) - p+=line([(0,-5),(0,5)],thickness=3,linestyle='dashed',color='red') - p.SHOW_OPTIONS['xmin']=-5 - p - + + + + +
@@ -150,61 +153,55 @@
Graph of y=\sin(x) - - -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) - + + + + +
Graph of y=\csc x - - -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) -for i in [-2..2]: - p+=line([(i*pi,-2*pi),(i*pi,2*pi)],thickness=3,linestyle='dashed',color='red') -p - + + + + +
Graph of y=\cos x - - -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) - + + + + +
Graph of y=\sec x - - -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 - + + + + +
Graph of y=\tan x - - -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 - + + + + +
Graph of y=\cot x - - -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 - + + + + +
@@ -215,61 +212,55 @@ p
Graph of y=\sin^{-1}(x) - - p=plot(arcsin(x),xmin=-1,xmax=1,ymin=-pi,ymax=pi,thickness=3,aspect_ratio=1,detect_poles=True,gridlines=True, ticks=[1,pi/4],tick_formatter=[SR(1),pi]) - p.SHOW_OPTIONS['xmin']=-pi - p.SHOW_OPTIONS['xmax']=pi - p - + + + + +
Graph of y=\csc^{-1}(x) - - p=plot(arccsc(x),xmin=-pi,xmax=-1,ymin=-pi,ymax=pi,thickness=3,aspect_ratio=1,detect_poles=True,gridlines=True, ticks=[1,pi/4],tick_formatter=[SR(1),pi]) - p+=plot(arccsc(x),xmin=1,xmax=pi,ymin=-pi,ymax=pi,thickness=3,aspect_ratio=1,detect_poles=True,gridlines=True, ticks=[1,pi/4],tick_formatter=[SR(1),pi]) - p+=line([(-pi,0),(pi,0)],thickness=3,linestyle='dashed',color='red') - p - + + + + +
Graph of y=\cos^{-1}(x) - - p=plot(arccos(x),xmin=-1,xmax=1,ymin=-pi,ymax=pi,thickness=3,aspect_ratio=1,detect_poles=True,gridlines=True, ticks=[1,pi/4],tick_formatter=[SR(1),pi]) - p.SHOW_OPTIONS['xmin']=-pi - p.SHOW_OPTIONS['xmax']=pi - p - + + + + +
Graph of y=\sec^{-1}(x) - - p=plot(arcsec(x),xmin=-pi,xmax=-1,ymin=-pi,ymax=pi,thickness=3,aspect_ratio=1,detect_poles=True,gridlines=True, ticks=[1,pi/4],tick_formatter=[SR(1),pi]) - p+=plot(arcsec(x),xmin=1,xmax=pi,ymin=-pi,ymax=pi,thickness=3,aspect_ratio=1,detect_poles=True,gridlines=True, ticks=[1,pi/4],tick_formatter=[SR(1),pi]) - p+=line([(-pi,pi/2),(pi,pi/2)],thickness=3,linestyle='dashed',color='red') - p - + + + + +
Graph of y=\tan^{-1}(x) - - p=plot(arctan(x),xmin=-pi,xmax=pi,ymin=-pi,ymax=pi,thickness=3,aspect_ratio=1,detect_poles=True,gridlines=True, ticks=[1,pi/4],tick_formatter=[SR(1),pi]) - p+=line([(-pi,pi/2),(pi,pi/2)],thickness=3,linestyle='dashed',color='red') - p+=line([(-pi,-pi/2),(pi,-pi/2)],thickness=3,linestyle='dashed',color='red') - p - + + + + +
Graph of y=\cot^{-1}(x) - - p=plot(arccot(x),xmin=-pi,xmax=-0.001,ymin=-pi,ymax=pi,thickness=3,aspect_ratio=1,detect_poles=True,gridlines=True, ticks=[1,pi/4],tick_formatter=[SR(1),pi]) - p+=plot(arccot(x),xmin=0.001,xmax=pi,ymin=-pi,ymax=pi,thickness=3,aspect_ratio=1,detect_poles=True,gridlines=True, ticks=[1,pi/4],tick_formatter=[SR(1),pi]) - p+=line([(-pi,0),(pi,0)],thickness=3,linestyle='dashed',color='red') - p - + + + + +
diff --git a/source/precalculus/source/meta/prefigure/graph-absolute.xml b/source/precalculus/source/meta/prefigure/graph-absolute.xml new file mode 100644 index 000000000..bdc31387b --- /dev/null +++ b/source/precalculus/source/meta/prefigure/graph-absolute.xml @@ -0,0 +1,12 @@ + + f(x)=fabs(x) + + + + + + + + + + \ No newline at end of file diff --git a/source/precalculus/source/meta/prefigure/graph-arccos.xml b/source/precalculus/source/meta/prefigure/graph-arccos.xml new file mode 100644 index 000000000..93d3b34fe --- /dev/null +++ b/source/precalculus/source/meta/prefigure/graph-arccos.xml @@ -0,0 +1,12 @@ + + f(x)=acos(x) + + + + + + + + + + \ No newline at end of file diff --git a/source/precalculus/source/meta/prefigure/graph-arccot.xml b/source/precalculus/source/meta/prefigure/graph-arccot.xml new file mode 100644 index 000000000..fb177aa07 --- /dev/null +++ b/source/precalculus/source/meta/prefigure/graph-arccot.xml @@ -0,0 +1,19 @@ + + f(x)=atan(1/x) + + + + + + + + + + + + + + + + + \ No newline at end of file diff --git a/source/precalculus/source/meta/prefigure/graph-arccsc.xml b/source/precalculus/source/meta/prefigure/graph-arccsc.xml new file mode 100644 index 000000000..28eefac07 --- /dev/null +++ b/source/precalculus/source/meta/prefigure/graph-arccsc.xml @@ -0,0 +1,16 @@ + + f(x)=asin(1/x) + + + + + + + + + + + + + + \ No newline at end of file diff --git a/source/precalculus/source/meta/prefigure/graph-arcsec.xml b/source/precalculus/source/meta/prefigure/graph-arcsec.xml new file mode 100644 index 000000000..b20813c6f --- /dev/null +++ b/source/precalculus/source/meta/prefigure/graph-arcsec.xml @@ -0,0 +1,16 @@ + + f(x)=acos(1/x) + + + + + + + + + + + + + + \ No newline at end of file diff --git a/source/precalculus/source/meta/prefigure/graph-arcsin.xml b/source/precalculus/source/meta/prefigure/graph-arcsin.xml new file mode 100644 index 000000000..3a2807e92 --- /dev/null +++ b/source/precalculus/source/meta/prefigure/graph-arcsin.xml @@ -0,0 +1,12 @@ + + f(x)=asin(x) + + + + + + + + + + \ No newline at end of file diff --git a/source/precalculus/source/meta/prefigure/graph-arctan.xml b/source/precalculus/source/meta/prefigure/graph-arctan.xml new file mode 100644 index 000000000..2cc07ff61 --- /dev/null +++ b/source/precalculus/source/meta/prefigure/graph-arctan.xml @@ -0,0 +1,18 @@ + + f(x)=atan(x) + + + + + + + + + + + + + + + + \ No newline at end of file diff --git a/source/precalculus/source/meta/prefigure/graph-cos.xml b/source/precalculus/source/meta/prefigure/graph-cos.xml new file mode 100644 index 000000000..089d047c9 --- /dev/null +++ b/source/precalculus/source/meta/prefigure/graph-cos.xml @@ -0,0 +1,12 @@ + + f(x)=cos(x) + + + + + + + + + + \ No newline at end of file diff --git a/source/precalculus/source/meta/prefigure/graph-cot.xml b/source/precalculus/source/meta/prefigure/graph-cot.xml new file mode 100644 index 000000000..0c18fd78e --- /dev/null +++ b/source/precalculus/source/meta/prefigure/graph-cot.xml @@ -0,0 +1,24 @@ + + f(x)=1/tan(x) + + + + + + + + + + + + + + + + + + + + + + \ No newline at end of file diff --git a/source/precalculus/source/meta/prefigure/graph-csc.xml b/source/precalculus/source/meta/prefigure/graph-csc.xml new file mode 100644 index 000000000..e96206eb1 --- /dev/null +++ b/source/precalculus/source/meta/prefigure/graph-csc.xml @@ -0,0 +1,24 @@ + + f(x)=1/sin(x) + + + + + + + + + + + + + + + + + + + + + + \ No newline at end of file diff --git a/source/precalculus/source/meta/prefigure/graph-exponential.xml b/source/precalculus/source/meta/prefigure/graph-exponential.xml new file mode 100644 index 000000000..2349a2ce2 --- /dev/null +++ b/source/precalculus/source/meta/prefigure/graph-exponential.xml @@ -0,0 +1,16 @@ + + f(x)=2^x + + + + + + + + + + + + + + \ No newline at end of file diff --git a/source/precalculus/source/meta/prefigure/graph-exponentiale.xml b/source/precalculus/source/meta/prefigure/graph-exponentiale.xml new file mode 100644 index 000000000..7ab95850f --- /dev/null +++ b/source/precalculus/source/meta/prefigure/graph-exponentiale.xml @@ -0,0 +1,16 @@ + + f(x)=e^x + + + + + + + + + + + + + + \ No newline at end of file diff --git a/source/precalculus/source/meta/prefigure/graph-logarithm-natural.xml b/source/precalculus/source/meta/prefigure/graph-logarithm-natural.xml new file mode 100644 index 000000000..9f7b5e044 --- /dev/null +++ b/source/precalculus/source/meta/prefigure/graph-logarithm-natural.xml @@ -0,0 +1,16 @@ + + f(x)=log(x) + + + + + + + + + + + + + + \ No newline at end of file diff --git a/source/precalculus/source/meta/prefigure/graph-logarithm.xml b/source/precalculus/source/meta/prefigure/graph-logarithm.xml new file mode 100644 index 000000000..e4b8a9c6c --- /dev/null +++ b/source/precalculus/source/meta/prefigure/graph-logarithm.xml @@ -0,0 +1,16 @@ + + f(x)=log(x)/log(2) + + + + + + + + + + + + + + \ No newline at end of file diff --git a/source/precalculus/source/meta/prefigure/graph-sec.xml b/source/precalculus/source/meta/prefigure/graph-sec.xml new file mode 100644 index 000000000..a51d4ec05 --- /dev/null +++ b/source/precalculus/source/meta/prefigure/graph-sec.xml @@ -0,0 +1,22 @@ + + f(x)=1/cos(x) + + + + + + + + + + + + + + + + + + + + \ No newline at end of file diff --git a/source/precalculus/source/meta/prefigure/graph-sin.xml b/source/precalculus/source/meta/prefigure/graph-sin.xml new file mode 100644 index 000000000..ce17bb23f --- /dev/null +++ b/source/precalculus/source/meta/prefigure/graph-sin.xml @@ -0,0 +1,12 @@ + + f(x)=sin(x) + + + + + + + + + + \ No newline at end of file diff --git a/source/precalculus/source/meta/prefigure/graph-square-root.xml b/source/precalculus/source/meta/prefigure/graph-square-root.xml new file mode 100644 index 000000000..dd96c3150 --- /dev/null +++ b/source/precalculus/source/meta/prefigure/graph-square-root.xml @@ -0,0 +1,12 @@ + + f(x)=sqrt(x) + + + + + + + + + + \ No newline at end of file diff --git a/source/precalculus/source/meta/prefigure/graph-tan.xml b/source/precalculus/source/meta/prefigure/graph-tan.xml new file mode 100644 index 000000000..734b370fb --- /dev/null +++ b/source/precalculus/source/meta/prefigure/graph-tan.xml @@ -0,0 +1,22 @@ + + f(x)=tan(x) + + + + + + + + + + + + + + + + + + + + \ No newline at end of file diff --git a/source/precalculus/source/meta/prefigure/graphx-minus1.xml b/source/precalculus/source/meta/prefigure/graphx-minus1.xml new file mode 100644 index 000000000..c10169525 --- /dev/null +++ b/source/precalculus/source/meta/prefigure/graphx-minus1.xml @@ -0,0 +1,18 @@ + + f(x)=x^(-1) + + + + + + + + + + + + + + + + \ No newline at end of file diff --git a/source/precalculus/source/meta/prefigure/graphx-minus2.xml b/source/precalculus/source/meta/prefigure/graphx-minus2.xml new file mode 100644 index 000000000..bfe239545 --- /dev/null +++ b/source/precalculus/source/meta/prefigure/graphx-minus2.xml @@ -0,0 +1,18 @@ + + f(x)=x^(-2) + + + + + + + + + + + + + + + + \ No newline at end of file diff --git a/source/precalculus/source/meta/prefigure/graphx-minus3.xml b/source/precalculus/source/meta/prefigure/graphx-minus3.xml new file mode 100644 index 000000000..3fc4b893d --- /dev/null +++ b/source/precalculus/source/meta/prefigure/graphx-minus3.xml @@ -0,0 +1,18 @@ + + f(x)=x^(-3) + + + + + + + + + + + + + + + + \ No newline at end of file diff --git a/source/precalculus/source/meta/prefigure/graphx-minus4.xml b/source/precalculus/source/meta/prefigure/graphx-minus4.xml new file mode 100644 index 000000000..651c0f04c --- /dev/null +++ b/source/precalculus/source/meta/prefigure/graphx-minus4.xml @@ -0,0 +1,18 @@ + + f(x)=x^(-3) + + + + + + + + + + + + + + + + \ No newline at end of file diff --git a/source/precalculus/source/meta/prefigure/graphx.xml b/source/precalculus/source/meta/prefigure/graphx.xml new file mode 100644 index 000000000..b1d7308a4 --- /dev/null +++ b/source/precalculus/source/meta/prefigure/graphx.xml @@ -0,0 +1,12 @@ + + f(x)=x + + + + + + + + + + \ No newline at end of file diff --git a/source/precalculus/source/meta/prefigure/graphx2.xml b/source/precalculus/source/meta/prefigure/graphx2.xml new file mode 100644 index 000000000..074613453 --- /dev/null +++ b/source/precalculus/source/meta/prefigure/graphx2.xml @@ -0,0 +1,12 @@ + + f(x)=x^2 + + + + + + + + + + \ No newline at end of file diff --git a/source/precalculus/source/meta/prefigure/graphx3.xml b/source/precalculus/source/meta/prefigure/graphx3.xml new file mode 100644 index 000000000..0187b56b9 --- /dev/null +++ b/source/precalculus/source/meta/prefigure/graphx3.xml @@ -0,0 +1,12 @@ + + f(x)=x^3 + + + + + + + + + + \ No newline at end of file diff --git a/source/precalculus/source/meta/prefigure/graphx4.xml b/source/precalculus/source/meta/prefigure/graphx4.xml new file mode 100644 index 000000000..95bd0fff8 --- /dev/null +++ b/source/precalculus/source/meta/prefigure/graphx4.xml @@ -0,0 +1,12 @@ + + f(x)=x^3 + + + + + + + + + + \ No newline at end of file From 86182899207010f7766ac44fece611c1df614925 Mon Sep 17 00:00:00 2001 From: Drew Lewis Date: Tue, 27 Jan 2026 18:26:23 +0000 Subject: [PATCH 02/12] PF1 images --- source/precalculus/source/07-PF/01.ptx | 317 ++++++++---------- .../PF1-compound-transformation1.xml | 12 + .../PF1-compound-transformation2.xml | 12 + .../PF1-compound-transformation3.xml | 12 + .../PF1-compound-transformation4.xml | 12 + .../07-PF/prefigure/PF1-cosine-one-period.xml | 13 + .../07-PF/prefigure/PF1-cosine-points.xml | 21 ++ .../source/07-PF/prefigure/PF1-fluency1.xml | 15 + .../source/07-PF/prefigure/PF1-fluency2.xml | 15 + .../07-PF/prefigure/PF1-graph-activity1.xml | 12 + .../07-PF/prefigure/PF1-graph-activity2.xml | 12 + .../07-PF/prefigure/PF1-graph-activity3.xml | 12 + .../07-PF/prefigure/PF1-sin-one-period.xml | 13 + .../07-PF/prefigure/PF1-sine-points.xml | 21 ++ .../prefigure/PF1-sine-transformation1.xml | 15 + .../prefigure/PF1-sine-transformation2.xml | 15 + .../prefigure/PF1-sine-transformation3.xml | 15 + .../prefigure/PF1-sine-transformation4.xml | 15 + .../prefigure/PF1-sine-transformation5.xml | 15 + .../prefigure/PF1-sine-transformation6.xml | 15 + .../prefigure/PF1-sine-transformation7.xml | 15 + .../prefigure/PF1-sine-transformation8.xml | 15 + .../source/07-PF/prefigure/PF1-sine.xml | 13 + 23 files changed, 446 insertions(+), 186 deletions(-) create mode 100644 source/precalculus/source/07-PF/prefigure/PF1-compound-transformation1.xml create mode 100644 source/precalculus/source/07-PF/prefigure/PF1-compound-transformation2.xml create mode 100644 source/precalculus/source/07-PF/prefigure/PF1-compound-transformation3.xml create mode 100644 source/precalculus/source/07-PF/prefigure/PF1-compound-transformation4.xml create mode 100644 source/precalculus/source/07-PF/prefigure/PF1-cosine-one-period.xml create mode 100644 source/precalculus/source/07-PF/prefigure/PF1-cosine-points.xml create mode 100644 source/precalculus/source/07-PF/prefigure/PF1-fluency1.xml create mode 100644 source/precalculus/source/07-PF/prefigure/PF1-fluency2.xml create mode 100644 source/precalculus/source/07-PF/prefigure/PF1-graph-activity1.xml create mode 100644 source/precalculus/source/07-PF/prefigure/PF1-graph-activity2.xml create mode 100644 source/precalculus/source/07-PF/prefigure/PF1-graph-activity3.xml create mode 100644 source/precalculus/source/07-PF/prefigure/PF1-sin-one-period.xml create mode 100644 source/precalculus/source/07-PF/prefigure/PF1-sine-points.xml create mode 100644 source/precalculus/source/07-PF/prefigure/PF1-sine-transformation1.xml create mode 100644 source/precalculus/source/07-PF/prefigure/PF1-sine-transformation2.xml create mode 100644 source/precalculus/source/07-PF/prefigure/PF1-sine-transformation3.xml create mode 100644 source/precalculus/source/07-PF/prefigure/PF1-sine-transformation4.xml create mode 100644 source/precalculus/source/07-PF/prefigure/PF1-sine-transformation5.xml create mode 100644 source/precalculus/source/07-PF/prefigure/PF1-sine-transformation6.xml create mode 100644 source/precalculus/source/07-PF/prefigure/PF1-sine-transformation7.xml create mode 100644 source/precalculus/source/07-PF/prefigure/PF1-sine-transformation8.xml create mode 100644 source/precalculus/source/07-PF/prefigure/PF1-sine.xml diff --git a/source/precalculus/source/07-PF/01.ptx b/source/precalculus/source/07-PF/01.ptx index a8d12a6bd..b69aaeb22 100644 --- a/source/precalculus/source/07-PF/01.ptx +++ b/source/precalculus/source/07-PF/01.ptx @@ -239,16 +239,10 @@

- - -P=TBIL.trig_plot(sin(x),(x,0,2*pi),ticks=pi/6) -for i in [0..12]: - P+=point((pi*i/6,sin(pi*i/6)),pointsize=50,color='blue') -for i in [0..8]: - P+=point((pi*i/4,sin(pi*i/4)),pointsize=50,color='blue') -P - - + + + +

@@ -468,10 +462,9 @@ P

- - -TBIL.trig_plot(sin(x),(x,-2*pi,4*pi),ticks=pi/2) - + + +

@@ -518,43 +511,34 @@ TBIL.trig_plot(sin(x),(x,-2*pi,4*pi),ticks=pi/2)

Which of the following graphs represents one cycle of h(x)=\sin 2x. (To help compare the functions, one cycle of f(x)=\sin x is shown as a dashed line on each graph.)

    -
  1. - - -P=TBIL.trig_plot(sin(x),(x,0,2*pi),ticks=pi/2,thickness=1,linestyle="--") -P+=TBIL.trig_plot(2*sin(x),(x,0,2*pi),ticks=pi/2,thickness=3) -P - -
  2. - - -P=TBIL.trig_plot(sin(x),(x,0,2*pi),ticks=pi/2,thickness=1,linestyle="--") -P+=TBIL.trig_plot(sin(2*x),(x,0,2*pi),ticks=pi/2,thickness=3) -P - + + + -
    3. -
  3. - - -P=TBIL.trig_plot(sin(x),(x,0,2*pi),ticks=pi/2,thickness=1,linestyle="--") -P+=TBIL.trig_plot(sin(x/2),(x,0,2*pi),ticks=pi/2,thickness=3) -P - -
    4. - -
  4. - - -P=TBIL.trig_plot(sin(x),(x,0,2*pi),ticks=pi/2,thickness=1,linestyle="--") -P+=TBIL.trig_plot(sin(x)+2,(x,0,2*pi),ticks=pi/2,thickness=3) -P - -
    5. - - + +
  5. + + + + + +
    6. +
  6. + + + + + +
    7. +
  7. + + + + + +

@@ -599,43 +583,34 @@ P

Which of the following graphs represents one cycle of j(x)=\sin \frac{1}{2}x. (To help compare the functions, one cycle of f(x)=\sin x is shown as a dashed line on each graph.)

    -
  1. - - -P=TBIL.trig_plot(sin(x),(x,0,2*pi),ticks=pi/2,thickness=1,linestyle="--") -P+=TBIL.trig_plot(2*sin(x),(x,0,2*pi),ticks=pi/2,thickness=3) -P - -
  2. - - -P=TBIL.trig_plot(sin(x),(x,0,2*pi),ticks=pi/2,thickness=1,linestyle="--") -P+=TBIL.trig_plot(sin(2*x),(x,0,2*pi),ticks=pi/2,thickness=3) -P - + + + -
    3. -
  3. - - -P=TBIL.trig_plot(sin(x),(x,0,2*pi),ticks=pi/2,thickness=1,linestyle="--") -P+=TBIL.trig_plot(sin(x/2),(x,0,2*pi),ticks=pi/2,thickness=3) -P - -
    4. - -
  4. - - -P=TBIL.trig_plot(sin(x),(x,0,2*pi),ticks=pi/2,thickness=1,linestyle="--") -P+=TBIL.trig_plot(sin(x)+2,(x,0,2*pi),ticks=pi/2,thickness=3) -P - -
    5. - - + +
  5. + + + + + +
    6. +
  6. + + + + + +
    7. +
  7. + + + + + +

@@ -682,41 +657,34 @@ P

Which of the following graphs represents one cycle of k(x)=\sin \left(x+\dfrac{\pi}{2}\right). (To help compare the functions, one cycle of f(x)=\sin x is shown as a dashed line on each graph.)

    -
  1. - - -P=TBIL.trig_plot(sin(x),(x,0,2*pi),ticks=pi/2,thickness=1,linestyle="--") -P+=TBIL.trig_plot(sin(x-pi/2),(x,pi/2,5/2*pi),ticks=pi/2,thickness=3) -P - -
    2. - -
  2. - - -P=TBIL.trig_plot(sin(x),(x,0,2*pi),ticks=pi/2,thickness=1,linestyle="--") -P+=TBIL.trig_plot(sin(x+pi/2),(x,-pi/2,3/2*pi),ticks=pi/2,thickness=3) -P - -
    3. - -
  3. - - -P=TBIL.trig_plot(sin(x),(x,0,2*pi),ticks=pi/2,thickness=1,linestyle="--") -P+=TBIL.trig_plot(sin(x)+pi/2,(x,0,2*pi),ticks=pi/2,thickness=3) -P - -
    4. -
  4. - - -P=TBIL.trig_plot(sin(x),(x,0,2*pi),ticks=pi/2,thickness=1,linestyle="--") -P+=TBIL.trig_plot(sin(x)-pi/2,(x,0,2*pi),ticks=pi/2,thickness=3) -P - -
    5. - +
  5. + + + + + +
    6. +
  6. + + + + + +
    7. +
  7. + + + + + +
    8. +
  8. + + + + + +

@@ -956,16 +924,10 @@ P

- - -P=TBIL.trig_plot(cos(x),(x,0,2*pi),ticks=pi/6) -for i in [0..12]: - P+=point((pi*i/6,cos(pi*i/6)),pointsize=50,color='blue') -for i in [0..8]: - P+=point((pi*i/4,cos(pi*i/4)),pointsize=50,color='blue') -P - - + + + +

@@ -1002,22 +964,18 @@ P Now that we can graph both the standard sine and cosine curves, we can add them to our list of parent functions in . We also show them graphed below on the interval [0,2\pi].

- f(x)=\sin x - - - -TBIL.trig_plot(sin(x),(x,0,2*pi),ticks=pi/2) - - + + + + +

- f(x)=\cos x - - - -TBIL.trig_plot(cos(x),(x,0,2*pi),ticks=pi/2) - - + + + + +

@@ -1032,14 +990,11 @@ TBIL.trig_plot(cos(x),(x,0,2*pi),ticks=pi/2)

- - - -P=TBIL.trig_plot(sin(x),(-pi/2,5/2*pi),ticks=pi/2,thickness=1,linestyle="--") -P+=TBIL.trig_plot(2*sin(x-pi/2), (-pi/2,5/2*pi),ticks=pi/2) -P - - + + + + +

@@ -1057,14 +1012,11 @@ P

- - - -P=TBIL.trig_plot(sin(x),(-pi/2,5/2*pi),ticks=pi/2,thickness=1,linestyle="--") -P+=TBIL.trig_plot(1/2*sin(2*x+2*pi), (-pi/2,5/2*pi),ticks=pi/2) -P - - + + + + +

@@ -1075,7 +1027,7 @@ P Period: \pi

- Phase shift: -\pi or \pi + Phase shift: -\frac{\pi}{2} or \frac{\pi}{2}

@@ -1223,10 +1175,9 @@ P - - -TBIL.trig_plot(sin(2*x),(-2*pi,2*pi)) - + + + @@ -1236,10 +1187,9 @@ TBIL.trig_plot(sin(2*x),(-2*pi,2*pi)) - - -TBIL.trig_plot(sin(2*(x-pi/2)),(-2*pi,2*pi)) - + + + @@ -1249,10 +1199,9 @@ TBIL.trig_plot(sin(2*(x-pi/2)),(-2*pi,2*pi)) - - -TBIL.trig_plot(3*sin(2*(x-pi/2)),(-2*pi,2*pi)) - + + + @@ -1262,10 +1211,9 @@ TBIL.trig_plot(3*sin(2*(x-pi/2)),(-2*pi,2*pi)) - - -TBIL.trig_plot(3*sin(2*(x-pi/2))-3,(-2*pi,2*pi)) - + + + @@ -1281,10 +1229,9 @@ TBIL.trig_plot(3*sin(2*(x-pi/2))-3,(-2*pi,2*pi)) - - -TBIL.trig_plot(2*sin(3*x-pi)+4,(-2*pi,2*pi),ymin=0) - + + + @@ -1294,10 +1241,9 @@ TBIL.trig_plot(2*sin(3*x-pi)+4,(-2*pi,2*pi),ymin=0) - - -TBIL.trig_plot(4*cos(2*x+2*pi)+1,(-2*pi,2*pi)) - + + + @@ -1307,10 +1253,9 @@ TBIL.trig_plot(4*cos(2*x+2*pi)+1,(-2*pi,2*pi)) - - -TBIL.trig_plot(-3*sin(4*x-pi/2)+1,(-2*pi,2*pi)) - + + + diff --git a/source/precalculus/source/07-PF/prefigure/PF1-compound-transformation1.xml b/source/precalculus/source/07-PF/prefigure/PF1-compound-transformation1.xml new file mode 100644 index 000000000..c89d06e5b --- /dev/null +++ b/source/precalculus/source/07-PF/prefigure/PF1-compound-transformation1.xml @@ -0,0 +1,12 @@ + + f(x)=sin(2*x) + + + + + + + + + + \ No newline at end of file diff --git a/source/precalculus/source/07-PF/prefigure/PF1-compound-transformation2.xml b/source/precalculus/source/07-PF/prefigure/PF1-compound-transformation2.xml new file mode 100644 index 000000000..e9776e68d --- /dev/null +++ b/source/precalculus/source/07-PF/prefigure/PF1-compound-transformation2.xml @@ -0,0 +1,12 @@ + + f(x)=sin(2*(x-pi/2)) + + + + + + + + + + \ No newline at end of file diff --git a/source/precalculus/source/07-PF/prefigure/PF1-compound-transformation3.xml b/source/precalculus/source/07-PF/prefigure/PF1-compound-transformation3.xml new file mode 100644 index 000000000..c0bfc46e5 --- /dev/null +++ b/source/precalculus/source/07-PF/prefigure/PF1-compound-transformation3.xml @@ -0,0 +1,12 @@ + + f(x)=3*sin(2*(x-pi/2)) + + + + + + + + + + \ No newline at end of file diff --git a/source/precalculus/source/07-PF/prefigure/PF1-compound-transformation4.xml b/source/precalculus/source/07-PF/prefigure/PF1-compound-transformation4.xml new file mode 100644 index 000000000..5c602dc54 --- /dev/null +++ b/source/precalculus/source/07-PF/prefigure/PF1-compound-transformation4.xml @@ -0,0 +1,12 @@ + + f(x)=3*sin(2*(x-pi/2))-3 + + + + + + + + + + \ No newline at end of file diff --git a/source/precalculus/source/07-PF/prefigure/PF1-cosine-one-period.xml b/source/precalculus/source/07-PF/prefigure/PF1-cosine-one-period.xml new file mode 100644 index 000000000..b1d11f9f2 --- /dev/null +++ b/source/precalculus/source/07-PF/prefigure/PF1-cosine-one-period.xml @@ -0,0 +1,13 @@ + + f(x)=cos(x) + + + + + + + + + + + \ No newline at end of file diff --git a/source/precalculus/source/07-PF/prefigure/PF1-cosine-points.xml b/source/precalculus/source/07-PF/prefigure/PF1-cosine-points.xml new file mode 100644 index 000000000..b4e8bb310 --- /dev/null +++ b/source/precalculus/source/07-PF/prefigure/PF1-cosine-points.xml @@ -0,0 +1,21 @@ + + f(x)=cos(x) + + + + + + + + + + + + + + + + + + + \ No newline at end of file diff --git a/source/precalculus/source/07-PF/prefigure/PF1-fluency1.xml b/source/precalculus/source/07-PF/prefigure/PF1-fluency1.xml new file mode 100644 index 000000000..3bbc13670 --- /dev/null +++ b/source/precalculus/source/07-PF/prefigure/PF1-fluency1.xml @@ -0,0 +1,15 @@ + + f(x)=sin(x) + h(x)=2*sin(x-pi/2) + + + + + + + + + + + + \ No newline at end of file diff --git a/source/precalculus/source/07-PF/prefigure/PF1-fluency2.xml b/source/precalculus/source/07-PF/prefigure/PF1-fluency2.xml new file mode 100644 index 000000000..8b33cbd8d --- /dev/null +++ b/source/precalculus/source/07-PF/prefigure/PF1-fluency2.xml @@ -0,0 +1,15 @@ + + f(x)=sin(x) + h(x)=1/2*sin(2*x+pi) + + + + + + + + + + + + \ No newline at end of file diff --git a/source/precalculus/source/07-PF/prefigure/PF1-graph-activity1.xml b/source/precalculus/source/07-PF/prefigure/PF1-graph-activity1.xml new file mode 100644 index 000000000..2d03b953e --- /dev/null +++ b/source/precalculus/source/07-PF/prefigure/PF1-graph-activity1.xml @@ -0,0 +1,12 @@ + + f(x)=2*sin(3*x-pi)+4 + + + + + + + + + + \ No newline at end of file diff --git a/source/precalculus/source/07-PF/prefigure/PF1-graph-activity2.xml b/source/precalculus/source/07-PF/prefigure/PF1-graph-activity2.xml new file mode 100644 index 000000000..c58eff221 --- /dev/null +++ b/source/precalculus/source/07-PF/prefigure/PF1-graph-activity2.xml @@ -0,0 +1,12 @@ + + f(x)=4*cos(2*x+2*pi)+1 + + + + + + + + + + \ No newline at end of file diff --git a/source/precalculus/source/07-PF/prefigure/PF1-graph-activity3.xml b/source/precalculus/source/07-PF/prefigure/PF1-graph-activity3.xml new file mode 100644 index 000000000..ea4342d49 --- /dev/null +++ b/source/precalculus/source/07-PF/prefigure/PF1-graph-activity3.xml @@ -0,0 +1,12 @@ + + f(x)=-3*sin(4*x-pi/2)+1 + + + + + + + + + + \ No newline at end of file diff --git a/source/precalculus/source/07-PF/prefigure/PF1-sin-one-period.xml b/source/precalculus/source/07-PF/prefigure/PF1-sin-one-period.xml new file mode 100644 index 000000000..93f49cf44 --- /dev/null +++ b/source/precalculus/source/07-PF/prefigure/PF1-sin-one-period.xml @@ -0,0 +1,13 @@ + + f(x)=sin(x) + + + + + + + + + + + \ No newline at end of file diff --git a/source/precalculus/source/07-PF/prefigure/PF1-sine-points.xml b/source/precalculus/source/07-PF/prefigure/PF1-sine-points.xml new file mode 100644 index 000000000..a80685557 --- /dev/null +++ b/source/precalculus/source/07-PF/prefigure/PF1-sine-points.xml @@ -0,0 +1,21 @@ + + f(x)=sin(x) + + + + + + + + + + + + + + + + + + + \ No newline at end of file diff --git a/source/precalculus/source/07-PF/prefigure/PF1-sine-transformation1.xml b/source/precalculus/source/07-PF/prefigure/PF1-sine-transformation1.xml new file mode 100644 index 000000000..a13a4aece --- /dev/null +++ b/source/precalculus/source/07-PF/prefigure/PF1-sine-transformation1.xml @@ -0,0 +1,15 @@ + + f(x)=sin(x) + h(x)=2*sin(x) + + + + + + + + + + + + \ No newline at end of file diff --git a/source/precalculus/source/07-PF/prefigure/PF1-sine-transformation2.xml b/source/precalculus/source/07-PF/prefigure/PF1-sine-transformation2.xml new file mode 100644 index 000000000..2596d295b --- /dev/null +++ b/source/precalculus/source/07-PF/prefigure/PF1-sine-transformation2.xml @@ -0,0 +1,15 @@ + + f(x)=sin(x) + h(x)=sin(2*x) + + + + + + + + + + + + \ No newline at end of file diff --git a/source/precalculus/source/07-PF/prefigure/PF1-sine-transformation3.xml b/source/precalculus/source/07-PF/prefigure/PF1-sine-transformation3.xml new file mode 100644 index 000000000..7cbf36f23 --- /dev/null +++ b/source/precalculus/source/07-PF/prefigure/PF1-sine-transformation3.xml @@ -0,0 +1,15 @@ + + f(x)=sin(x) + h(x)=sin(1/2*x) + + + + + + + + + + + + \ No newline at end of file diff --git a/source/precalculus/source/07-PF/prefigure/PF1-sine-transformation4.xml b/source/precalculus/source/07-PF/prefigure/PF1-sine-transformation4.xml new file mode 100644 index 000000000..831f0e0c8 --- /dev/null +++ b/source/precalculus/source/07-PF/prefigure/PF1-sine-transformation4.xml @@ -0,0 +1,15 @@ + + f(x)=sin(x) + h(x)=sin(x)+2 + + + + + + + + + + + + \ No newline at end of file diff --git a/source/precalculus/source/07-PF/prefigure/PF1-sine-transformation5.xml b/source/precalculus/source/07-PF/prefigure/PF1-sine-transformation5.xml new file mode 100644 index 000000000..ac56e3f63 --- /dev/null +++ b/source/precalculus/source/07-PF/prefigure/PF1-sine-transformation5.xml @@ -0,0 +1,15 @@ + + f(x)=sin(x) + h(x)=sin(x-pi/2) + + + + + + + + + + + + \ No newline at end of file diff --git a/source/precalculus/source/07-PF/prefigure/PF1-sine-transformation6.xml b/source/precalculus/source/07-PF/prefigure/PF1-sine-transformation6.xml new file mode 100644 index 000000000..f14825f43 --- /dev/null +++ b/source/precalculus/source/07-PF/prefigure/PF1-sine-transformation6.xml @@ -0,0 +1,15 @@ + + f(x)=sin(x) + h(x)=sin(x+pi/2) + + + + + + + + + + + + \ No newline at end of file diff --git a/source/precalculus/source/07-PF/prefigure/PF1-sine-transformation7.xml b/source/precalculus/source/07-PF/prefigure/PF1-sine-transformation7.xml new file mode 100644 index 000000000..74ac44efc --- /dev/null +++ b/source/precalculus/source/07-PF/prefigure/PF1-sine-transformation7.xml @@ -0,0 +1,15 @@ + + f(x)=sin(x) + h(x)=sin(x)+pi/2 + + + + + + + + + + + + \ No newline at end of file diff --git a/source/precalculus/source/07-PF/prefigure/PF1-sine-transformation8.xml b/source/precalculus/source/07-PF/prefigure/PF1-sine-transformation8.xml new file mode 100644 index 000000000..b1a7e680f --- /dev/null +++ b/source/precalculus/source/07-PF/prefigure/PF1-sine-transformation8.xml @@ -0,0 +1,15 @@ + + f(x)=sin(x) + h(x)=sin(x)-pi/2 + + + + + + + + + + + + \ No newline at end of file diff --git a/source/precalculus/source/07-PF/prefigure/PF1-sine.xml b/source/precalculus/source/07-PF/prefigure/PF1-sine.xml new file mode 100644 index 000000000..358182213 --- /dev/null +++ b/source/precalculus/source/07-PF/prefigure/PF1-sine.xml @@ -0,0 +1,13 @@ + + f(x)=sin(x) + + + + + + + + + + + \ No newline at end of file From b4b4028a832c953d5c88b5f8b364494b07287884 Mon Sep 17 00:00:00 2001 From: Drew Lewis Date: Tue, 27 Jan 2026 18:31:08 +0000 Subject: [PATCH 03/12] Filename typo --- .../source/07-PF/prefigure/PF1-sine-one-period.xml | 13 +++++++++++++ 1 file changed, 13 insertions(+) create mode 100644 source/precalculus/source/07-PF/prefigure/PF1-sine-one-period.xml diff --git a/source/precalculus/source/07-PF/prefigure/PF1-sine-one-period.xml b/source/precalculus/source/07-PF/prefigure/PF1-sine-one-period.xml new file mode 100644 index 000000000..93f49cf44 --- /dev/null +++ b/source/precalculus/source/07-PF/prefigure/PF1-sine-one-period.xml @@ -0,0 +1,13 @@ + + f(x)=sin(x) + + + + + + + + + + + \ No newline at end of file From 0a7eaa63a5c6845695232d855ab924153371c5af Mon Sep 17 00:00:00 2001 From: Drew Lewis Date: Tue, 27 Jan 2026 18:31:24 +0000 Subject: [PATCH 04/12] Remove old file --- .../source/07-PF/prefigure/PF1-sin-one-period.xml | 13 ------------- 1 file changed, 13 deletions(-) delete mode 100644 source/precalculus/source/07-PF/prefigure/PF1-sin-one-period.xml diff --git a/source/precalculus/source/07-PF/prefigure/PF1-sin-one-period.xml b/source/precalculus/source/07-PF/prefigure/PF1-sin-one-period.xml deleted file mode 100644 index 93f49cf44..000000000 --- a/source/precalculus/source/07-PF/prefigure/PF1-sin-one-period.xml +++ /dev/null @@ -1,13 +0,0 @@ - - f(x)=sin(x) - - - - - - - - - - - \ No newline at end of file From 16283e7b7ab54174b0a1999837c3e732ff8b45c9 Mon Sep 17 00:00:00 2001 From: Drew Lewis Date: Tue, 27 Jan 2026 21:59:58 +0000 Subject: [PATCH 05/12] PF2 graphs --- source/precalculus/source/07-PF/02.ptx | 242 +++++++----------- .../source/07-PF/prefigure/PF2-graph-cot.xml | 18 ++ .../source/07-PF/prefigure/PF2-graph-cot2.xml | 21 ++ .../07-PF/prefigure/PF2-graph-csc-sin.xml | 25 ++ .../source/07-PF/prefigure/PF2-graph-csc.xml | 18 ++ .../07-PF/prefigure/PF2-graph-fluency.xml | 19 ++ .../07-PF/prefigure/PF2-graph-sec-cos.xml | 24 ++ .../prefigure/PF2-graph-secant-points.xml | 25 ++ .../07-PF/prefigure/PF2-graph-tan-points.xml | 25 ++ .../source/07-PF/prefigure/PF2-graph-tan2.xml | 20 ++ .../07-PF/prefigure/PF2-sec-transform1.xml | 20 ++ .../07-PF/prefigure/PF2-sec-transform2.xml | 20 ++ .../07-PF/prefigure/PF2-sec-transform3.xml | 21 ++ .../07-PF/prefigure/PF2-sec-transform4.xml | 21 ++ .../source/07-PF/prefigure/PF2-tan2x.xml | 19 ++ 15 files changed, 392 insertions(+), 146 deletions(-) create mode 100644 source/precalculus/source/07-PF/prefigure/PF2-graph-cot.xml create mode 100644 source/precalculus/source/07-PF/prefigure/PF2-graph-cot2.xml create mode 100644 source/precalculus/source/07-PF/prefigure/PF2-graph-csc-sin.xml create mode 100644 source/precalculus/source/07-PF/prefigure/PF2-graph-csc.xml create mode 100644 source/precalculus/source/07-PF/prefigure/PF2-graph-fluency.xml create mode 100644 source/precalculus/source/07-PF/prefigure/PF2-graph-sec-cos.xml create mode 100644 source/precalculus/source/07-PF/prefigure/PF2-graph-secant-points.xml create mode 100644 source/precalculus/source/07-PF/prefigure/PF2-graph-tan-points.xml create mode 100644 source/precalculus/source/07-PF/prefigure/PF2-graph-tan2.xml create mode 100644 source/precalculus/source/07-PF/prefigure/PF2-sec-transform1.xml create mode 100644 source/precalculus/source/07-PF/prefigure/PF2-sec-transform2.xml create mode 100644 source/precalculus/source/07-PF/prefigure/PF2-sec-transform3.xml create mode 100644 source/precalculus/source/07-PF/prefigure/PF2-sec-transform4.xml create mode 100644 source/precalculus/source/07-PF/prefigure/PF2-tan2x.xml diff --git a/source/precalculus/source/07-PF/02.ptx b/source/precalculus/source/07-PF/02.ptx index b7bba8bef..fd4d71c70 100644 --- a/source/precalculus/source/07-PF/02.ptx +++ b/source/precalculus/source/07-PF/02.ptx @@ -245,19 +245,11 @@

- - - -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 - - + + + + +

@@ -543,19 +535,11 @@ P

- - - -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 - - + + + + +

@@ -619,17 +603,14 @@ P for every point (a,b) on the graph of \cos(x), the point (a,\frac{1}{b}) is on the graph of \sec(x).

-
- y=\sec(x) - - -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 - -
+
+ y=\sec(x) + + + + + +
@@ -649,11 +630,10 @@ p

Recall the graph of \sin(x)

- - - -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) - + + + +
@@ -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

- - -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 - - + + + +

@@ -788,17 +763,14 @@ P for every point (a,b) on the graph of \sin(x), the point (a,\frac{1}{b}) is on the graph of \csc(x).

-
- y=\csc(x) - - -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 - -
+
+ y=\csc(x) + + + + + +
@@ -813,17 +785,7 @@ p

Recall the graph of \tan(x)

-
- - - -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 - - -
+

\ldots,-2\pi,-\pi,0,\pi,2\pi,\ldots

@@ -885,16 +847,11 @@ P

It may be helpful to first sketch the graph of \tan(x).

- - - -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 - - + + + + +

@@ -958,28 +915,24 @@ P for every point (a,b) on the graph of \tan(x), the point (a,\frac{1}{b}) is on the graph of \cot(x).

- -
- y=\tan(x) - - -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 - -
-
- y=\cot(x) - - -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 - -
- + +
+ y=\tan(x) + + + + + +
+
+ y=\cot(x) + + + + + +
+ @@ -1013,33 +966,34 @@ p

Which of the following is the graph of g(x)=\sec\left(x+\dfrac{\pi}{2}\right)?

    -
  1. - -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 -
    2. -
  2. - -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 -
    3. -
  3. - -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 -
  4. - -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 -
    5. +
  5. + + + + + +
    6. +
  6. + + + + + +
    7. +
  7. + + + + + +
    8. +
  8. + + + + + +
@@ -1139,13 +1093,11 @@ p

Graph h(x)=\tan(2x).

- - -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 - + + + + + @@ -1209,13 +1161,11 @@ p

Graph k(x)=3\csc\left(\dfrac{x}{2}\right).

- - - 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 - + + + + + diff --git a/source/precalculus/source/07-PF/prefigure/PF2-graph-cot.xml b/source/precalculus/source/07-PF/prefigure/PF2-graph-cot.xml new file mode 100644 index 000000000..b0215c9a9 --- /dev/null +++ b/source/precalculus/source/07-PF/prefigure/PF2-graph-cot.xml @@ -0,0 +1,18 @@ + + f(x)=1/tan(x) + + + + + + + + + + + + + + + + \ No newline at end of file diff --git a/source/precalculus/source/07-PF/prefigure/PF2-graph-cot2.xml b/source/precalculus/source/07-PF/prefigure/PF2-graph-cot2.xml new file mode 100644 index 000000000..bc34f0a45 --- /dev/null +++ b/source/precalculus/source/07-PF/prefigure/PF2-graph-cot2.xml @@ -0,0 +1,21 @@ + + f(x)=1/tan(x) + + + + + + + + + + + + + + + + + + + \ No newline at end of file diff --git a/source/precalculus/source/07-PF/prefigure/PF2-graph-csc-sin.xml b/source/precalculus/source/07-PF/prefigure/PF2-graph-csc-sin.xml new file mode 100644 index 000000000..cd314812a --- /dev/null +++ b/source/precalculus/source/07-PF/prefigure/PF2-graph-csc-sin.xml @@ -0,0 +1,25 @@ + + f(x)=1/sin(x) + g(x)=sin(x) + + + + + + + + + + + + + + + + + + + + + + \ No newline at end of file diff --git a/source/precalculus/source/07-PF/prefigure/PF2-graph-csc.xml b/source/precalculus/source/07-PF/prefigure/PF2-graph-csc.xml new file mode 100644 index 000000000..6ca297729 --- /dev/null +++ b/source/precalculus/source/07-PF/prefigure/PF2-graph-csc.xml @@ -0,0 +1,18 @@ + + f(x)=1/sin(x) + + + + + + + + + + + + + + + + \ No newline at end of file diff --git a/source/precalculus/source/07-PF/prefigure/PF2-graph-fluency.xml b/source/precalculus/source/07-PF/prefigure/PF2-graph-fluency.xml new file mode 100644 index 000000000..2539611ee --- /dev/null +++ b/source/precalculus/source/07-PF/prefigure/PF2-graph-fluency.xml @@ -0,0 +1,19 @@ + + f(x)=3/sin(x/2) + + + + + + + + + + + + + + + + + \ No newline at end of file diff --git a/source/precalculus/source/07-PF/prefigure/PF2-graph-sec-cos.xml b/source/precalculus/source/07-PF/prefigure/PF2-graph-sec-cos.xml new file mode 100644 index 000000000..d76fae037 --- /dev/null +++ b/source/precalculus/source/07-PF/prefigure/PF2-graph-sec-cos.xml @@ -0,0 +1,24 @@ + + f(x)=1/cos(x) + g(x)=cos(x) + + + + + + + + + + + + + + + + + + + + + \ No newline at end of file diff --git a/source/precalculus/source/07-PF/prefigure/PF2-graph-secant-points.xml b/source/precalculus/source/07-PF/prefigure/PF2-graph-secant-points.xml new file mode 100644 index 000000000..fdf77023b --- /dev/null +++ b/source/precalculus/source/07-PF/prefigure/PF2-graph-secant-points.xml @@ -0,0 +1,25 @@ + + f(x)=1/cos(x) + + + + + + + + + + + + + + + + + + + + + + + \ No newline at end of file diff --git a/source/precalculus/source/07-PF/prefigure/PF2-graph-tan-points.xml b/source/precalculus/source/07-PF/prefigure/PF2-graph-tan-points.xml new file mode 100644 index 000000000..5254ccc9e --- /dev/null +++ b/source/precalculus/source/07-PF/prefigure/PF2-graph-tan-points.xml @@ -0,0 +1,25 @@ + + f(x)=tan(x) + + + + + + + + + + + + + + + + + + + + + + + \ No newline at end of file diff --git a/source/precalculus/source/07-PF/prefigure/PF2-graph-tan2.xml b/source/precalculus/source/07-PF/prefigure/PF2-graph-tan2.xml new file mode 100644 index 000000000..0730c9402 --- /dev/null +++ b/source/precalculus/source/07-PF/prefigure/PF2-graph-tan2.xml @@ -0,0 +1,20 @@ + + f(x)=tan(x) + + + + + + + + + + + + + + + + + + \ No newline at end of file diff --git a/source/precalculus/source/07-PF/prefigure/PF2-sec-transform1.xml b/source/precalculus/source/07-PF/prefigure/PF2-sec-transform1.xml new file mode 100644 index 000000000..033551716 --- /dev/null +++ b/source/precalculus/source/07-PF/prefigure/PF2-sec-transform1.xml @@ -0,0 +1,20 @@ + + f(x)=1/cos(x) + + + + + + + + + + + + + + + + + + \ No newline at end of file diff --git a/source/precalculus/source/07-PF/prefigure/PF2-sec-transform2.xml b/source/precalculus/source/07-PF/prefigure/PF2-sec-transform2.xml new file mode 100644 index 000000000..118739086 --- /dev/null +++ b/source/precalculus/source/07-PF/prefigure/PF2-sec-transform2.xml @@ -0,0 +1,20 @@ + + f(x)=1/cos(x+pi) + + + + + + + + + + + + + + + + + + \ No newline at end of file diff --git a/source/precalculus/source/07-PF/prefigure/PF2-sec-transform3.xml b/source/precalculus/source/07-PF/prefigure/PF2-sec-transform3.xml new file mode 100644 index 000000000..1d57af0fd --- /dev/null +++ b/source/precalculus/source/07-PF/prefigure/PF2-sec-transform3.xml @@ -0,0 +1,21 @@ + + f(x)=1/cos(x-pi/2) + + + + + + + + + + + + + + + + + + + \ No newline at end of file diff --git a/source/precalculus/source/07-PF/prefigure/PF2-sec-transform4.xml b/source/precalculus/source/07-PF/prefigure/PF2-sec-transform4.xml new file mode 100644 index 000000000..e94a79f15 --- /dev/null +++ b/source/precalculus/source/07-PF/prefigure/PF2-sec-transform4.xml @@ -0,0 +1,21 @@ + + f(x)=1/cos(x+pi/2) + + + + + + + + + + + + + + + + + + + \ No newline at end of file diff --git a/source/precalculus/source/07-PF/prefigure/PF2-tan2x.xml b/source/precalculus/source/07-PF/prefigure/PF2-tan2x.xml new file mode 100644 index 000000000..eb285a57a --- /dev/null +++ b/source/precalculus/source/07-PF/prefigure/PF2-tan2x.xml @@ -0,0 +1,19 @@ + + f(x)=tan(2*x) + + + + + + + + + + + + + + + + + \ No newline at end of file From 1badf8dfb20ce7ab3aa4b6c4f5c0e96f525eca07 Mon Sep 17 00:00:00 2001 From: Drew Lewis Date: Tue, 27 Jan 2026 22:02:40 +0000 Subject: [PATCH 06/12] Rename file --- .../{PF2-graph-secant-points.xml => PF2-graph-sec-points.xml} | 0 1 file changed, 0 insertions(+), 0 deletions(-) rename source/precalculus/source/07-PF/prefigure/{PF2-graph-secant-points.xml => PF2-graph-sec-points.xml} (100%) diff --git a/source/precalculus/source/07-PF/prefigure/PF2-graph-secant-points.xml b/source/precalculus/source/07-PF/prefigure/PF2-graph-sec-points.xml similarity index 100% rename from source/precalculus/source/07-PF/prefigure/PF2-graph-secant-points.xml rename to source/precalculus/source/07-PF/prefigure/PF2-graph-sec-points.xml From e449c0efd663e39033a394d4acc9f1b02948f3af Mon Sep 17 00:00:00 2001 From: Drew Lewis Date: Tue, 27 Jan 2026 22:51:58 +0000 Subject: [PATCH 07/12] PF3 graphs --- source/precalculus/source/07-PF/03.ptx | 180 ++++++++++++------------- 1 file changed, 85 insertions(+), 95 deletions(-) diff --git a/source/precalculus/source/07-PF/03.ptx b/source/precalculus/source/07-PF/03.ptx index 6fbf218b9..bc8050ae8 100644 --- a/source/precalculus/source/07-PF/03.ptx +++ b/source/precalculus/source/07-PF/03.ptx @@ -39,17 +39,11 @@ Which of the following equations determines the angle of the ramp, which the carpenter will use to set his saw?

- -p=Graphics() -p+=line([(0,0),(48,0),(48,4),(0,0)],thickness="1",color="black") -p+=text(r"$\theta$", (15,0.6),fontsize=10,color="black") -p+=arc((0,0),14.3,sector=(0,arctan(1/12)),color="black") -p+=text("$4$",(48.5,2),fontsize=10,color="black") -p+=text("$48$",(24,2.6),fontsize=10,color="black") -p.axes(False) -p.set_aspect_ratio(1) -p - + + + + +
  1. \sin(\theta)=\frac{1}{12}
  2. \cos(\theta)=\frac{1}{12}
    3. @@ -84,31 +78,35 @@ p

    1. 0 \leq x \leq \pi

      -

      - -TBIL.trig_plot(sin(x),(x,0,pi),ymin=-1,ymax=1,ticks=[pi/2,1],thickness=2) -

      + + + + +

    2. -\dfrac{\pi}{2} \leq x \leq \dfrac{\pi}{2}

      -

      - -TBIL.trig_plot(sin(x),(x,-pi/2,pi/2),ymin=-1,ymax=1,ticks=[pi/2,1],thickness=2) -

      + + + + +

    3. 0 \leq x \leq 2\pi

      -

      - -TBIL.trig_plot(sin(x),(x,0,2*pi),ymin=-1,ymax=1,ticks=[pi/2,1],thickness=2) -

      + + + + +

    4. -\pi \leq x \leq \pi

      -

      - -TBIL.trig_plot(sin(x),(x,-pi,pi),ymin=-1,ymax=1,ticks=[pi/2,1],thickness=2) -

      + + + + +
    @@ -182,31 +180,35 @@ TBIL.trig_plot(sin(x),(x,-pi,pi),ymin=-1,ymax=1,ticks=[pi/2,1],thickness=2)

    1. 0 \leq x \leq \pi

      -

      - -TBIL.trig_plot(cos(x),(x,0,pi),ymin=-1,ymax=1,ticks=[pi/2,1],thickness=2) -

      + + + + +

    2. -\dfrac{\pi}{2} \leq x \leq \dfrac{\pi}{2}

      -

      - -TBIL.trig_plot(cos(x),(x,-pi/2,pi/2),ymin=-1,ymax=1,ticks=[pi/2,1],thickness=2) -

      + + + + +

    3. 0 \leq x \leq 2\pi

      -

      - -TBIL.trig_plot(cos(x),(x,0,2*pi),ymin=-1,ymax=1,ticks=[pi/2,1],thickness=2) -

      + + + + +

    4. -\pi \leq x \leq \pi

      -

      - -TBIL.trig_plot(cos(x),(x,-pi,pi),ymin=-1,ymax=1,ticks=[pi/2,1],thickness=2) -

      + + + + +
    @@ -272,31 +274,35 @@ TBIL.trig_plot(cos(x),(x,-pi,pi),ymin=-1,ymax=1,ticks=[pi/2,1],thickness=2)

    1. 0 \leq x \leq \pi

      -

      - -TBIL.trig_plot(tan(x),(x,0,pi),ymin=-3,ymax=3,ticks=[pi/2,1],thickness=2, detect_poles=True) -

      + + + + +

    2. -\dfrac{\pi}{2} \leq x \leq \dfrac{\pi}{2}

      -

      - -TBIL.trig_plot(tan(x),(x,-pi/2,pi/2),ymin=-3,ymax=3,ticks=[pi/2,1],thickness=2) -

      + + + + +

    3. 0 \leq x \leq 2\pi

      -

      - -TBIL.trig_plot(tan(x),(x,0,2*pi),ymin=-3,ymax=3,ticks=[pi/2,1],thickness=2,detect_poles=True) -

      + + + + +

    4. -\pi \leq x \leq \pi

      -

      - -TBIL.trig_plot(tan(x),(x,-pi,pi),ymin=-3,ymax=3,ticks=[pi/2,1],thickness=2,detect_poles=True) -

      + + + + +
    @@ -506,14 +512,11 @@ TBIL.trig_plot(tan(x),(x,-pi,pi),ymin=-3,ymax=3,ticks=[pi/2,1],thickness=2,detec

    - -p=plot(arcsin(x),xmin=-1,xmax=1,ymin=-pi,ymax=pi,thickness=3,aspect_ratio=1,detect_poles=True,gridlines=True, ticks=[1,pi/4],tick_formatter=[SR(1),pi]) -for xval in [-1,-sqrt(3)/2,-sqrt(2)/2,-1/2,0,1/2,sqrt(2)/2,sqrt(3)/2,1]: - p+=point((xval,arcsin(xval)),pointsize=50,color="blue") -p.SHOW_OPTIONS['xmin']=-pi -p.SHOW_OPTIONS['xmax']=pi -p - + + + + + @@ -639,14 +642,11 @@ p

    - -p=plot(arccos(x),xmin=-1,xmax=1,ymin=-pi,ymax=pi,thickness=3,aspect_ratio=1,detect_poles=True,gridlines=True, ticks=[1,pi/4],tick_formatter=[SR(1),pi]) -for xval in [-1,-sqrt(3)/2,-sqrt(2)/2,-1/2,0,1/2,sqrt(2)/2,sqrt(3)/2,1]: - p+=point((xval,arccos(xval)),pointsize=50,color="blue") -p.SHOW_OPTIONS['xmin']=-pi -p.SHOW_OPTIONS['xmax']=pi -p - + + + + +     @@ -756,14 +756,11 @@ p

    - -p=plot(arctan(x),xmin=-pi,xmax=pi,ymin=-pi,ymax=pi,thickness=3,aspect_ratio=1,detect_poles=True,gridlines=True, ticks=[1,pi/4],tick_formatter=[SR(1),pi]) -for xval in [-sqrt(3),-1,-1/sqrt(3),0,1/sqrt(3),1,sqrt(3)]: - p+=point((xval,arctan(xval)),pointsize=50,color="blue") -p.SHOW_OPTIONS['xmin']=-pi -p.SHOW_OPTIONS['xmax']=pi -p - + + + + +     @@ -812,18 +809,11 @@ p

    - - p=Graphics() - p+=line([(0,0),(12,0),(12,5),(0,0)],thickness="1",color="black") - p+=text(r"$\theta$", (11.5,3.8),fontsize=15,color="black") - p+=arc((12,5),1,sector=(3*pi/2-arccos(5/12),3*pi/2),color="black") - p+=text("$5$",(12.2,2.5),fontsize=15,color="black") - p+=text("$13$",(6,2.8),fontsize=15,color="black") - p+=text("$12$",(6,-0.3),fontsize=15,color="blue") - p.axes(False) - p.set_aspect_ratio(1) - p - + + + + +     From 97779b05c6f9594740e97a018431e1886395b158 Mon Sep 17 00:00:00 2001 From: Drew Lewis Date: Tue, 27 Jan 2026 22:53:59 +0000 Subject: [PATCH 08/12] PF3 graphs --- .../07-PF/prefigure/PF3-cos-restriction1.xml | 12 +++++++++++ .../07-PF/prefigure/PF3-cos-restriction2.xml | 12 +++++++++++ .../07-PF/prefigure/PF3-cos-restriction3.xml | 12 +++++++++++ .../07-PF/prefigure/PF3-cos-restriction4.xml | 12 +++++++++++ .../07-PF/prefigure/PF3-graph-arccos.xml | 20 +++++++++++++++++++ .../07-PF/prefigure/PF3-graph-arcsin.xml | 20 +++++++++++++++++++ .../07-PF/prefigure/PF3-graph-arctan.xml | 20 +++++++++++++++++++ .../07-PF/prefigure/PF3-sin-restriction1.xml | 12 +++++++++++ .../07-PF/prefigure/PF3-sin-restriction2.xml | 12 +++++++++++ .../07-PF/prefigure/PF3-sin-restriction3.xml | 12 +++++++++++ .../07-PF/prefigure/PF3-sin-restriction4.xml | 12 +++++++++++ .../07-PF/prefigure/PF3-tan-restriction1.xml | 12 +++++++++++ .../07-PF/prefigure/PF3-tan-restriction2.xml | 12 +++++++++++ .../07-PF/prefigure/PF3-tan-restriction3.xml | 12 +++++++++++ .../07-PF/prefigure/PF3-tan-restriction4.xml | 12 +++++++++++ .../source/07-PF/prefigure/PF3-triangle.xml | 18 +++++++++++++++++ .../source/07-PF/prefigure/PF3-triangle2.xml | 18 +++++++++++++++++ 17 files changed, 240 insertions(+) create mode 100644 source/precalculus/source/07-PF/prefigure/PF3-cos-restriction1.xml create mode 100644 source/precalculus/source/07-PF/prefigure/PF3-cos-restriction2.xml create mode 100644 source/precalculus/source/07-PF/prefigure/PF3-cos-restriction3.xml create mode 100644 source/precalculus/source/07-PF/prefigure/PF3-cos-restriction4.xml create mode 100644 source/precalculus/source/07-PF/prefigure/PF3-graph-arccos.xml create mode 100644 source/precalculus/source/07-PF/prefigure/PF3-graph-arcsin.xml create mode 100644 source/precalculus/source/07-PF/prefigure/PF3-graph-arctan.xml create mode 100644 source/precalculus/source/07-PF/prefigure/PF3-sin-restriction1.xml create mode 100644 source/precalculus/source/07-PF/prefigure/PF3-sin-restriction2.xml create mode 100644 source/precalculus/source/07-PF/prefigure/PF3-sin-restriction3.xml create mode 100644 source/precalculus/source/07-PF/prefigure/PF3-sin-restriction4.xml create mode 100644 source/precalculus/source/07-PF/prefigure/PF3-tan-restriction1.xml create mode 100644 source/precalculus/source/07-PF/prefigure/PF3-tan-restriction2.xml create mode 100644 source/precalculus/source/07-PF/prefigure/PF3-tan-restriction3.xml create mode 100644 source/precalculus/source/07-PF/prefigure/PF3-tan-restriction4.xml create mode 100644 source/precalculus/source/07-PF/prefigure/PF3-triangle.xml create mode 100644 source/precalculus/source/07-PF/prefigure/PF3-triangle2.xml diff --git a/source/precalculus/source/07-PF/prefigure/PF3-cos-restriction1.xml b/source/precalculus/source/07-PF/prefigure/PF3-cos-restriction1.xml new file mode 100644 index 000000000..cae9d6323 --- /dev/null +++ b/source/precalculus/source/07-PF/prefigure/PF3-cos-restriction1.xml @@ -0,0 +1,12 @@ + + f(x)=cos(x) + + + + + + + + + + \ No newline at end of file diff --git a/source/precalculus/source/07-PF/prefigure/PF3-cos-restriction2.xml b/source/precalculus/source/07-PF/prefigure/PF3-cos-restriction2.xml new file mode 100644 index 000000000..ee810a837 --- /dev/null +++ b/source/precalculus/source/07-PF/prefigure/PF3-cos-restriction2.xml @@ -0,0 +1,12 @@ + + f(x)=cos(x) + + + + + + + + + + \ No newline at end of file diff --git a/source/precalculus/source/07-PF/prefigure/PF3-cos-restriction3.xml b/source/precalculus/source/07-PF/prefigure/PF3-cos-restriction3.xml new file mode 100644 index 000000000..4b6ae4c4e --- /dev/null +++ b/source/precalculus/source/07-PF/prefigure/PF3-cos-restriction3.xml @@ -0,0 +1,12 @@ + + f(x)=cos(x) + + + + + + + + + + \ No newline at end of file diff --git a/source/precalculus/source/07-PF/prefigure/PF3-cos-restriction4.xml b/source/precalculus/source/07-PF/prefigure/PF3-cos-restriction4.xml new file mode 100644 index 000000000..e647f5d05 --- /dev/null +++ b/source/precalculus/source/07-PF/prefigure/PF3-cos-restriction4.xml @@ -0,0 +1,12 @@ + + f(x)=cos(x) + + + + + + + + + + \ No newline at end of file diff --git a/source/precalculus/source/07-PF/prefigure/PF3-graph-arccos.xml b/source/precalculus/source/07-PF/prefigure/PF3-graph-arccos.xml new file mode 100644 index 000000000..bd0be5477 --- /dev/null +++ b/source/precalculus/source/07-PF/prefigure/PF3-graph-arccos.xml @@ -0,0 +1,20 @@ + + f(x)=acos(x) + + + + + + + + + + + + + + + + + + \ No newline at end of file diff --git a/source/precalculus/source/07-PF/prefigure/PF3-graph-arcsin.xml b/source/precalculus/source/07-PF/prefigure/PF3-graph-arcsin.xml new file mode 100644 index 000000000..088b1afad --- /dev/null +++ b/source/precalculus/source/07-PF/prefigure/PF3-graph-arcsin.xml @@ -0,0 +1,20 @@ + + f(x)=asin(x) + + + + + + + + + + + + + + + + + + \ No newline at end of file diff --git a/source/precalculus/source/07-PF/prefigure/PF3-graph-arctan.xml b/source/precalculus/source/07-PF/prefigure/PF3-graph-arctan.xml new file mode 100644 index 000000000..5c56d479e --- /dev/null +++ b/source/precalculus/source/07-PF/prefigure/PF3-graph-arctan.xml @@ -0,0 +1,20 @@ + + f(x)=atan(x) + + + + + + + + + + + + + + + + + + \ No newline at end of file diff --git a/source/precalculus/source/07-PF/prefigure/PF3-sin-restriction1.xml b/source/precalculus/source/07-PF/prefigure/PF3-sin-restriction1.xml new file mode 100644 index 000000000..5d1a67669 --- /dev/null +++ b/source/precalculus/source/07-PF/prefigure/PF3-sin-restriction1.xml @@ -0,0 +1,12 @@ + + f(x)=sin(x) + + + + + + + + + + \ No newline at end of file diff --git a/source/precalculus/source/07-PF/prefigure/PF3-sin-restriction2.xml b/source/precalculus/source/07-PF/prefigure/PF3-sin-restriction2.xml new file mode 100644 index 000000000..adb899bc0 --- /dev/null +++ b/source/precalculus/source/07-PF/prefigure/PF3-sin-restriction2.xml @@ -0,0 +1,12 @@ + + f(x)=sin(x) + + + + + + + + + + \ No newline at end of file diff --git a/source/precalculus/source/07-PF/prefigure/PF3-sin-restriction3.xml b/source/precalculus/source/07-PF/prefigure/PF3-sin-restriction3.xml new file mode 100644 index 000000000..ca3249418 --- /dev/null +++ b/source/precalculus/source/07-PF/prefigure/PF3-sin-restriction3.xml @@ -0,0 +1,12 @@ + + f(x)=sin(x) + + + + + + + + + + \ No newline at end of file diff --git a/source/precalculus/source/07-PF/prefigure/PF3-sin-restriction4.xml b/source/precalculus/source/07-PF/prefigure/PF3-sin-restriction4.xml new file mode 100644 index 000000000..6ab939b31 --- /dev/null +++ b/source/precalculus/source/07-PF/prefigure/PF3-sin-restriction4.xml @@ -0,0 +1,12 @@ + + f(x)=sin(x) + + + + + + + + + + \ No newline at end of file diff --git a/source/precalculus/source/07-PF/prefigure/PF3-tan-restriction1.xml b/source/precalculus/source/07-PF/prefigure/PF3-tan-restriction1.xml new file mode 100644 index 000000000..86ff6a585 --- /dev/null +++ b/source/precalculus/source/07-PF/prefigure/PF3-tan-restriction1.xml @@ -0,0 +1,12 @@ + + f(x)=tan(x) + + + + + + + + + + \ No newline at end of file diff --git a/source/precalculus/source/07-PF/prefigure/PF3-tan-restriction2.xml b/source/precalculus/source/07-PF/prefigure/PF3-tan-restriction2.xml new file mode 100644 index 000000000..377991cc6 --- /dev/null +++ b/source/precalculus/source/07-PF/prefigure/PF3-tan-restriction2.xml @@ -0,0 +1,12 @@ + + f(x)=tan(x) + + + + + + + + + + \ No newline at end of file diff --git a/source/precalculus/source/07-PF/prefigure/PF3-tan-restriction3.xml b/source/precalculus/source/07-PF/prefigure/PF3-tan-restriction3.xml new file mode 100644 index 000000000..c2410e52a --- /dev/null +++ b/source/precalculus/source/07-PF/prefigure/PF3-tan-restriction3.xml @@ -0,0 +1,12 @@ + + f(x)=tan(x) + + + + + + + + + + \ No newline at end of file diff --git a/source/precalculus/source/07-PF/prefigure/PF3-tan-restriction4.xml b/source/precalculus/source/07-PF/prefigure/PF3-tan-restriction4.xml new file mode 100644 index 000000000..a9334dcb5 --- /dev/null +++ b/source/precalculus/source/07-PF/prefigure/PF3-tan-restriction4.xml @@ -0,0 +1,12 @@ + + f(x)=tan(x) + + + + + + + + + + \ No newline at end of file diff --git a/source/precalculus/source/07-PF/prefigure/PF3-triangle.xml b/source/precalculus/source/07-PF/prefigure/PF3-triangle.xml new file mode 100644 index 000000000..b6a38d3cf --- /dev/null +++ b/source/precalculus/source/07-PF/prefigure/PF3-triangle.xml @@ -0,0 +1,18 @@ + + p1=(0,0) + p2=(48,0) + p3=(48,4) + + + + 48 + 4 + \theta + + + + + + + + \ No newline at end of file diff --git a/source/precalculus/source/07-PF/prefigure/PF3-triangle2.xml b/source/precalculus/source/07-PF/prefigure/PF3-triangle2.xml new file mode 100644 index 000000000..5af4b2997 --- /dev/null +++ b/source/precalculus/source/07-PF/prefigure/PF3-triangle2.xml @@ -0,0 +1,18 @@ + + p1=(0,0) + p2=(12,0) + p3=(12,5) + + + 12 + 13 + 5 + \theta + + + + + + + + \ No newline at end of file From 90c577246a7bb576e38c1e1d10c75e5c5f442b73 Mon Sep 17 00:00:00 2001 From: Drew Lewis Date: Tue, 27 Jan 2026 22:55:09 +0000 Subject: [PATCH 09/12] Missing namespace --- source/precalculus/source/07-PF/prefigure/PF3-triangle.xml | 2 +- source/precalculus/source/07-PF/prefigure/PF3-triangle2.xml | 2 +- 2 files changed, 2 insertions(+), 2 deletions(-) diff --git a/source/precalculus/source/07-PF/prefigure/PF3-triangle.xml b/source/precalculus/source/07-PF/prefigure/PF3-triangle.xml index b6a38d3cf..a2e0dd1c7 100644 --- a/source/precalculus/source/07-PF/prefigure/PF3-triangle.xml +++ b/source/precalculus/source/07-PF/prefigure/PF3-triangle.xml @@ -1,4 +1,4 @@ - + p1=(0,0) p2=(48,0) p3=(48,4) diff --git a/source/precalculus/source/07-PF/prefigure/PF3-triangle2.xml b/source/precalculus/source/07-PF/prefigure/PF3-triangle2.xml index 5af4b2997..4cb6eedeb 100644 --- a/source/precalculus/source/07-PF/prefigure/PF3-triangle2.xml +++ b/source/precalculus/source/07-PF/prefigure/PF3-triangle2.xml @@ -1,4 +1,4 @@ - + p1=(0,0) p2=(12,0) p3=(12,5) From 9a1e6dbbb27e93aba43eaf7c6da2ee167b6a0f26 Mon Sep 17 00:00:00 2001 From: Drew Lewis Date: Tue, 27 Jan 2026 23:03:21 +0000 Subject: [PATCH 10/12] Fix labels --- .../source/07-PF/prefigure/PF2-graph-sec-points.xml | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/source/precalculus/source/07-PF/prefigure/PF2-graph-sec-points.xml b/source/precalculus/source/07-PF/prefigure/PF2-graph-sec-points.xml index fdf77023b..7617a8a75 100644 --- a/source/precalculus/source/07-PF/prefigure/PF2-graph-sec-points.xml +++ b/source/precalculus/source/07-PF/prefigure/PF2-graph-sec-points.xml @@ -4,10 +4,10 @@ - + - + From 709ad4b4bc5925863cf6dce8181b9b040693f081 Mon Sep 17 00:00:00 2001 From: Drew Lewis Date: Wed, 28 Jan 2026 17:30:17 +0000 Subject: [PATCH 11/12] Fix some annotations --- .../07-PF/prefigure/PF1-cosine-points.xml | 14 +++++-------- .../07-PF/prefigure/PF1-sine-points.xml | 14 +++++-------- .../07-PF/prefigure/PF2-graph-sec-points.xml | 20 ++++++++----------- .../07-PF/prefigure/PF2-graph-tan-points.xml | 18 +++++++---------- 4 files changed, 25 insertions(+), 41 deletions(-) diff --git a/source/precalculus/source/07-PF/prefigure/PF1-cosine-points.xml b/source/precalculus/source/07-PF/prefigure/PF1-cosine-points.xml index b4e8bb310..e6489c6ff 100644 --- a/source/precalculus/source/07-PF/prefigure/PF1-cosine-points.xml +++ b/source/precalculus/source/07-PF/prefigure/PF1-cosine-points.xml @@ -1,20 +1,16 @@ f(x)=cos(x) + xs=[0,pi/6,pi/4,pi/3,pi/2,2*pi/3,3*pi/4,5*pi/6,pi,7*pi/6,5*pi/4,4*pi/3,3*pi/2,5*pi/3,7*pi/4,11*pi/6,2*pi] - - - - - - - - + + + - + diff --git a/source/precalculus/source/07-PF/prefigure/PF1-sine-points.xml b/source/precalculus/source/07-PF/prefigure/PF1-sine-points.xml index a80685557..e00e60852 100644 --- a/source/precalculus/source/07-PF/prefigure/PF1-sine-points.xml +++ b/source/precalculus/source/07-PF/prefigure/PF1-sine-points.xml @@ -1,20 +1,16 @@ f(x)=sin(x) + xs=[0,pi/6,pi/4,pi/3,pi/2,2*pi/3,3*pi/4,5*pi/6,pi,7*pi/6,5*pi/4,4*pi/3,3*pi/2,5*pi/3,7*pi/4,11*pi/6,2*pi] - - - - - - - - + + + - + diff --git a/source/precalculus/source/07-PF/prefigure/PF2-graph-sec-points.xml b/source/precalculus/source/07-PF/prefigure/PF2-graph-sec-points.xml index 7617a8a75..e4dd930e4 100644 --- a/source/precalculus/source/07-PF/prefigure/PF2-graph-sec-points.xml +++ b/source/precalculus/source/07-PF/prefigure/PF2-graph-sec-points.xml @@ -1,22 +1,18 @@ - - f(x)=1/cos(x) - + + f(x)=sec(x) + xs=[0,pi/6,pi/4,pi/3,pi/2,2*pi/3,3*pi/4,5*pi/6,pi,7*pi/6,5*pi/4,4*pi/3,3*pi/2,5*pi/3,7*pi/4,11*pi/6,2*pi] + - - - - - - - - + + + - + diff --git a/source/precalculus/source/07-PF/prefigure/PF2-graph-tan-points.xml b/source/precalculus/source/07-PF/prefigure/PF2-graph-tan-points.xml index 5254ccc9e..44cc058da 100644 --- a/source/precalculus/source/07-PF/prefigure/PF2-graph-tan-points.xml +++ b/source/precalculus/source/07-PF/prefigure/PF2-graph-tan-points.xml @@ -1,22 +1,18 @@ - + f(x)=tan(x) - + xs=[0,pi/6,pi/4,pi/3,pi/2,2*pi/3,3*pi/4,5*pi/6,pi,7*pi/6,5*pi/4,4*pi/3,3*pi/2,5*pi/3,7*pi/4,11*pi/6,2*pi] + - - - - - - - - + + + - + From 50abf63c60e7a264720b1ee04a866b3f74e6d9a5 Mon Sep 17 00:00:00 2001 From: Drew Lewis Date: Wed, 28 Jan 2026 17:58:52 +0000 Subject: [PATCH 12/12] Use new trig functions for better code readability --- source/precalculus/source/07-PF/prefigure/PF2-graph-cot.xml | 2 +- source/precalculus/source/07-PF/prefigure/PF2-graph-cot2.xml | 2 +- source/precalculus/source/07-PF/prefigure/PF2-graph-csc-sin.xml | 2 +- source/precalculus/source/07-PF/prefigure/PF2-graph-csc.xml | 2 +- source/precalculus/source/07-PF/prefigure/PF2-graph-sec-cos.xml | 2 +- .../precalculus/source/07-PF/prefigure/PF2-sec-transform1.xml | 2 +- .../precalculus/source/07-PF/prefigure/PF2-sec-transform2.xml | 2 +- .../precalculus/source/07-PF/prefigure/PF2-sec-transform3.xml | 2 +- .../precalculus/source/07-PF/prefigure/PF2-sec-transform4.xml | 2 +- 9 files changed, 9 insertions(+), 9 deletions(-) diff --git a/source/precalculus/source/07-PF/prefigure/PF2-graph-cot.xml b/source/precalculus/source/07-PF/prefigure/PF2-graph-cot.xml index b0215c9a9..c33d81886 100644 --- a/source/precalculus/source/07-PF/prefigure/PF2-graph-cot.xml +++ b/source/precalculus/source/07-PF/prefigure/PF2-graph-cot.xml @@ -1,5 +1,5 @@ - f(x)=1/tan(x) + f(x)=cot(x) diff --git a/source/precalculus/source/07-PF/prefigure/PF2-graph-cot2.xml b/source/precalculus/source/07-PF/prefigure/PF2-graph-cot2.xml index bc34f0a45..a4f63f474 100644 --- a/source/precalculus/source/07-PF/prefigure/PF2-graph-cot2.xml +++ b/source/precalculus/source/07-PF/prefigure/PF2-graph-cot2.xml @@ -1,5 +1,5 @@ - f(x)=1/tan(x) + f(x)=cot(x) diff --git a/source/precalculus/source/07-PF/prefigure/PF2-graph-csc-sin.xml b/source/precalculus/source/07-PF/prefigure/PF2-graph-csc-sin.xml index cd314812a..31387dd83 100644 --- a/source/precalculus/source/07-PF/prefigure/PF2-graph-csc-sin.xml +++ b/source/precalculus/source/07-PF/prefigure/PF2-graph-csc-sin.xml @@ -1,5 +1,5 @@ - f(x)=1/sin(x) + f(x)=csc(x) g(x)=sin(x) diff --git a/source/precalculus/source/07-PF/prefigure/PF2-graph-csc.xml b/source/precalculus/source/07-PF/prefigure/PF2-graph-csc.xml index 6ca297729..a90cc56a8 100644 --- a/source/precalculus/source/07-PF/prefigure/PF2-graph-csc.xml +++ b/source/precalculus/source/07-PF/prefigure/PF2-graph-csc.xml @@ -1,5 +1,5 @@ - f(x)=1/sin(x) + f(x)=csc(x) diff --git a/source/precalculus/source/07-PF/prefigure/PF2-graph-sec-cos.xml b/source/precalculus/source/07-PF/prefigure/PF2-graph-sec-cos.xml index d76fae037..7ce3e9c32 100644 --- a/source/precalculus/source/07-PF/prefigure/PF2-graph-sec-cos.xml +++ b/source/precalculus/source/07-PF/prefigure/PF2-graph-sec-cos.xml @@ -1,5 +1,5 @@ - f(x)=1/cos(x) + f(x)=sec(x) g(x)=cos(x) diff --git a/source/precalculus/source/07-PF/prefigure/PF2-sec-transform1.xml b/source/precalculus/source/07-PF/prefigure/PF2-sec-transform1.xml index 033551716..1a8ced133 100644 --- a/source/precalculus/source/07-PF/prefigure/PF2-sec-transform1.xml +++ b/source/precalculus/source/07-PF/prefigure/PF2-sec-transform1.xml @@ -1,5 +1,5 @@ - f(x)=1/cos(x) + f(x)=sec(x) diff --git a/source/precalculus/source/07-PF/prefigure/PF2-sec-transform2.xml b/source/precalculus/source/07-PF/prefigure/PF2-sec-transform2.xml index 118739086..4ea151d25 100644 --- a/source/precalculus/source/07-PF/prefigure/PF2-sec-transform2.xml +++ b/source/precalculus/source/07-PF/prefigure/PF2-sec-transform2.xml @@ -1,5 +1,5 @@ - f(x)=1/cos(x+pi) + f(x)=sec(x+pi) diff --git a/source/precalculus/source/07-PF/prefigure/PF2-sec-transform3.xml b/source/precalculus/source/07-PF/prefigure/PF2-sec-transform3.xml index 1d57af0fd..0216df377 100644 --- a/source/precalculus/source/07-PF/prefigure/PF2-sec-transform3.xml +++ b/source/precalculus/source/07-PF/prefigure/PF2-sec-transform3.xml @@ -1,5 +1,5 @@ - f(x)=1/cos(x-pi/2) + f(x)=sec(x-pi/2) diff --git a/source/precalculus/source/07-PF/prefigure/PF2-sec-transform4.xml b/source/precalculus/source/07-PF/prefigure/PF2-sec-transform4.xml index e94a79f15..e77a12fd0 100644 --- a/source/precalculus/source/07-PF/prefigure/PF2-sec-transform4.xml +++ b/source/precalculus/source/07-PF/prefigure/PF2-sec-transform4.xml @@ -1,5 +1,5 @@ - f(x)=1/cos(x+pi/2) + f(x)=sec(x+pi/2)