DuckieDai Trig 6 Graphs Python Program

trigonometry · MIT License

Overview

Graph any of the six trig functions in the form y = A*f(Bx - C) + D from one menu: amplitude or stretch, period, phase shift, midline, key points, and asymptotes, with a drawing on the calculator.

Owner-tested on a TI calculator
Version 1.0.0
3134 bytes
Uses math, ti_plotlib

Download TRIG6.py Read the source How to install

Before you run it

TI-84 Plus CE Python · No calculator OS or Python App version has been verified.
TI Connect CE .py transfer to the Python App; the owner's transfer details were not recorded
The function is y = A*f(Bx - C) + D for f = sin, cos, tan, csc, sec, or cot, with B not 0.
A, B, C, and D may be decimals, fractions such as 1/2, or multiples of pi such as pi/3 or -2pi.
Values are limited to -1,000,000 to 1,000,000; inf and nan are asked for again.

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Learn the math

How to graph all six trig functions with transformations

The idea

All six trig functions take the same four numbers in y = A*f(Bx - C) + D. A stretches the graph and flips it when negative, B changes the period, C/B slides it left or right, and D moves the midline. What changes from one function to the next is the period and where the key points and asymptotes fall.

Sine and cosine are waves with an amplitude. Cosecant and secant are 1 over sine and cosine, U-shaped branches with asymptotes where the wave crosses 0. Tangent and cotangent repeat every pi instead of every 2pi and climb from one asymptote to the next.

The formula

period = 2pi / |B| for sin, cos, csc, sec

period = pi / |B| for tan and cot

phase shift = C / B (right if positive, left if negative)

amplitude = |A| (sin and cos only); midline: y = D

A: the amplitude for sin and cos, or the stretch for the others; a negative A reflects the graph over the x-axis
B: sets the period; a negative B reflects it over the y-axis
C: together with B, the phase shift C/B
D: the midline

Using the program

Choose 1 to 6 for sin, cos, tan, csc, sec, or cot.
Type A, B, C, and D. Press Enter to keep the default in brackets. Fractions such as 1/2 and pi values such as pi/2 or -2pi work.
Read the amplitude or stretch, period, phase shift, midline, and any reflection.
Read the five key points. For tan, csc, sec, and cot some of them are vertical asymptotes, shown as VA: x = ...
Choose 1 at Draw? to see your graph in blue over the parent graph in gray, with the key points in red. Press clear to go back to the menu.

Worked example

Graph y = 2sec(x - pi/2). Choose 5, then type 2 for A, 1 for B, pi/2 for C, and 0 for D.

stretch = 2, period = 2pi, phase shift = pi/2 right, midline y = 0

The program shows No amplitude, Stretch: 2, Period: 2pi, and Phase: pi/2 right.

The key points are a quarter period, pi/2, apart: (pi/2, 2), VA: x = pi, (3pi/2, -2), VA: x = 2pi, and (5pi/2, 2).

Tips and common mistakes

Check the period first: tan and cot use pi, the other four use 2pi.
Only sin and cos have an amplitude. For csc and sec, |A| is where the branches turn around.
Divide C by B for the shift. In sec(2x - pi) the shift is pi/2, not pi.
Sketch the matching sine or cosine lightly first; csc and sec branches touch it at its tops and bottoms.

Where this comes up

Graphing all six transformed trig functions, with period, phase shift, and asymptotes, is the trigonometric graphs unit of precalculus and trigonometry.

Exact reviewed bytes

Source code

Download .py

View source below, copy it when JavaScript is available, or download the exact .py bytes.

from math import sin,cos,pi
N=('sin','cos','tan','csc','sec','cot')
def pg():input('[enter]');print('\n'*11)
def val(t):
 t=t.lower().replace(' ','').replace('*','')
 if 'pi' in t:
  a,b=(t+'/1').split('/')[:2]
  if not a.endswith('pi'):raise ValueError
  a=a[:-2];a={'':'1','+':'1','-':'-1'}.get(a,a)
  return float(a)*pi/float(b)
 if '/' in t:a,b=t.split('/');return float(a)/float(b)
 return float(t)
def ask(q,d):
 while 1:
  t=input(q+' ['+d+']: ').strip() or d
  try:
   v=val(t)
   if abs(v)<=1e6:return v
  except (ValueError,ZeroDivisionError):pass
  print('Like 2 or pi/3')
def num(x):
 if abs(x-round(x))<1e-8:return str(int(round(x)))
 for d in range(2,33):
  k=round(x*d)
  if abs(x*d-k)<1e-8:return str(int(k))+'/'+str(d)
 return str(round(x,4))
def rad(x):
 if abs(x)<1e-8:return '0'
 z=x/pi
 for d in range(1,65):
  k=int(round(z*d))
  if abs(z*d-k)<1e-8:return {1:'',-1:'-'}.get(k,str(k))+'pi'+('/'+str(d) if d>1 else '')
 return num(x)
def den(m,t):return cos(t) if m in(3,5) else sin(t) if m in(4,6) else 1
def trig(m,t):
 if abs(den(m,t))<1e-8:return None
 s=sin(t);c=cos(t)
 if m==1:return s
 if m==2:return c
 if m==3:return s/c
 if m==4:return 1/s
 if m==5:return 1/c
 return c/s
def draw(m,A,B,C,D,P,H,Q):
 try:
  import ti_plotlib as p
  lo=H-(3 if m==3 else 1)*P/4;hi=H+(3 if m==3 else 5)*P/4
  h=max(3,abs(D)+(1 if m<3 else 2.6)*max(1,abs(A))+1)
  p.cls();p.window(lo,hi,-h,h);p.axes('on')
  for k in(1,0):
   if k:p.color(140,140,140)
   else:p.color(0,0,255)
   o=None
   for i in range(91):
    x=lo+(hi-lo)*i/90;t=x if k else B*x-C;v=trig(m,t)
    y=v if k or v is None else D+A*v
    if y is not None and abs(y)<=h:
     if o and den(m,o[2])*den(m,t)>0:p.line(o[0],o[1],x,y,'')
     o=(x,y,t)
    else:o=None
  p.color(255,0,0)
  for x,y in Q:
   if y is not None and -h<=y<=h:p.plot(x,y,'o')
  p.show_plot()
 except Exception as e:print('No plot:',e);pg()
def main():
 print("TRIG 6 GRAPHS\n      __\n  ___(o )>  quack!\n  \\ <_. )\n   `---'\nDuckieDai (TM)\nhiddenwordscanner.com");pg()
 while 1:
  m=input('1 sin  2 cos  3 tan\n4 csc  5 sec  6 cot\n1-6, 7 Exit: ').strip()
  if m=='7':break
  if m not in('1','2','3','4','5','6'):continue
  m=int(m);print('y=A*'+N[m-1]+'(Bx-C)+D\n[enter] keeps default')
  A=ask('A','1');B=ask('B','1');C=ask('C','0');D=ask('D','0')
  if abs(B)<1e-12:print('B cannot be zero');pg();continue
  P=(pi if m in(3,6) else 2*pi)/abs(B);H=C/B;g=1 if B>0 else -1
  v=([0,g,0,-g,0],[1,0,-1,0,1],[None,-g,0,g,None],[None,g,None,-g,None],[1,None,-1,None,1],[None,g,0,-g,None])[m-1]
  Q=[(H+(i-2 if m==3 else i)*P/4,None if v[i] is None else D+A*v[i]) for i in range(5)]
  print('\n'*11)
  if m<3:print('Amplitude:',num(abs(A)))
  else:print('No amplitude\nStretch:',num(abs(A)))
  print('Period:',rad(P))
  print('Phase:',rad(abs(H)),'right' if H>1e-9 else 'left' if H<-1e-9 else 'none')
  print('Midline: y =',num(D))
  if A<0:print('Reflect x-axis')
  if B<0:print('Reflect y-axis')
  pg()
  for x,y in Q:print('VA: x = '+rad(x) if y is None else '('+rad(x)+', '+num(y)+')')
  pg()
  if input('Draw? 1 Yes 2 No: ').strip()=='1':draw(m,A,B,C,D,P,H,Q)
  print('\n'*11)
main()

from math import sin,cos,pi
N=('sin','cos','tan','csc','sec','cot')
def pg():input('[enter]');print('\n'*11)
def val(t):
t=t.lower().replace(' ','').replace('*','')
if 'pi' in t:
a,b=(t+'/1').split('/')[:2]
if not a.endswith('pi'):raise ValueError
a=a[:-2];a={'':'1','+':'1','-':'-1'}.get(a,a)
return float(a)*pi/float(b)
if '/' in t:a,b=t.split('/');return float(a)/float(b)
return float(t)
def ask(q,d):
while 1:
t=input(q+' ['+d+']: ').strip() or d
try:
v=val(t)
if abs(v)<=1e6:return v
except (ValueError,ZeroDivisionError):pass
print('Like 2 or pi/3')
def num(x):
if abs(x-round(x))<1e-8:return str(int(round(x)))
for d in range(2,33):
k=round(x*d)
if abs(x*d-k)<1e-8:return str(int(k))+'/'+str(d)
return str(round(x,4))
def rad(x):
if abs(x)<1e-8:return '0'
z=x/pi
for d in range(1,65):
k=int(round(z*d))
if abs(z*d-k)<1e-8:return {1:'',-1:'-'}.get(k,str(k))+'pi'+('/'+str(d) if d>1 else '')
return num(x)
def den(m,t):return cos(t) if m in(3,5) else sin(t) if m in(4,6) else 1
def trig(m,t):
if abs(den(m,t))<1e-8:return None
s=sin(t);c=cos(t)
if m==1:return s
if m==2:return c
if m==3:return s/c
if m==4:return 1/s
if m==5:return 1/c
return c/s
def draw(m,A,B,C,D,P,H,Q):
try:
import ti_plotlib as p
lo=H-(3 if m==3 else 1)*P/4;hi=H+(3 if m==3 else 5)*P/4
h=max(3,abs(D)+(1 if m<3 else 2.6)*max(1,abs(A))+1)
p.cls();p.window(lo,hi,-h,h);p.axes('on')
for k in(1,0):
if k:p.color(140,140,140)
else:p.color(0,0,255)
o=None
for i in range(91):
x=lo+(hi-lo)*i/90;t=x if k else B*x-C;v=trig(m,t)
y=v if k or v is None else D+A*v
if y is not None and abs(y)<=h:
if o and den(m,o[2])*den(m,t)>0:p.line(o[0],o[1],x,y,'')
o=(x,y,t)
else:o=None
p.color(255,0,0)
for x,y in Q:
if y is not None and -h<=y<=h:p.plot(x,y,'o')
p.show_plot()
except Exception as e:print('No plot:',e);pg()
def main():
print("TRIG 6 GRAPHS\n __\n ___(o )> quack!\n \\ <_. )\n `---'\nDuckieDai (TM)\nhiddenwordscanner.com");pg()
while 1:
m=input('1 sin 2 cos 3 tan\n4 csc 5 sec 6 cot\n1-6, 7 Exit: ').strip()
if m=='7':break
if m not in('1','2','3','4','5','6'):continue
m=int(m);print('y=A*'+N[m-1]+'(Bx-C)+D\n[enter] keeps default')
A=ask('A','1');B=ask('B','1');C=ask('C','0');D=ask('D','0')
if abs(B)<1e-12:print('B cannot be zero');pg();continue
P=(pi if m in(3,6) else 2*pi)/abs(B);H=C/B;g=1 if B>0 else -1
v=([0,g,0,-g,0],[1,0,-1,0,1],[None,-g,0,g,None],[None,g,None,-g,None],[1,None,-1,None,1],[None,g,0,-g,None])[m-1]
Q=[(H+(i-2 if m==3 else i)*P/4,None if v[i] is None else D+A*v[i]) for i in range(5)]
print('\n'*11)
if m<3:print('Amplitude:',num(abs(A)))
else:print('No amplitude\nStretch:',num(abs(A)))
print('Period:',rad(P))
print('Phase:',rad(abs(H)),'right' if H>1e-9 else 'left' if H<-1e-9 else 'none')
print('Midline: y =',num(D))
if A<0:print('Reflect x-axis')
if B<0:print('Reflect y-axis')
pg()
for x,y in Q:print('VA: x = '+rad(x) if y is None else '('+rad(x)+', '+num(y)+')')
pg()
if input('Draw? 1 Yes 2 No: ').strip()=='1':draw(m,A,B,C,D,P,H,Q)
print('\n'*11)
main()

Filename: TRIG6.py
Size: 3134 bytes
SHA-256: 2a214510ee4bd40a868136c7fd5a3e604a6b4be7ef1e7062c73eea406d9adc98

Usage

Inputs

A choice: 1 sin, 2 cos, 3 tan, 4 csc, 5 sec, 6 cot, 7 exit
A, B, C, and D for y = A*f(Bx - C) + D; Enter keeps the default shown

Outputs

The amplitude for sin and cos or the stretch for the other four, and the period, phase shift, midline, and any reflection
Five key x values: points, and vertical asymptotes for tan, csc, sec, and cot
Optionally, a graph on the calculator with the parent graph in gray and the key points marked

Units: Radians; angles may be typed as multiples of pi.

Assumptions and limitations

Assumptions

The function is y = A*f(Bx - C) + D for f = sin, cos, tan, csc, sec, or cot, with B not 0.
A, B, C, and D may be decimals, fractions such as 1/2, or multiples of pi such as pi/3 or -2pi.

Constraints

Values are limited to -1,000,000 to 1,000,000; inf and nan are asked for again.
B must not be 0. A B smaller than 0.000000000001 is treated as 0.

Known failures

Answers that are not a whole number, a fraction with a denominator up to 32, or a multiple of pi up to pi/64 show 4 decimal places.
The graph needs the calculator's ti_plotlib module; on a computer the program shows No plot instead.

Compatibility and review

Review status: Owner-tested on a TI calculator
Tested on: Owner reports personally running this program on a TI-84 Plus CE Python calculator; the test date, OS version, and Python App version were not recorded
What happened: Owner reported pass on the calculator for the owner's original. For publication, inf, nan, and values beyond 1,000,000 are asked for again instead of stopping the program. This exact file has not yet been rerun on a calculator.
Dependencies: math, ti_plotlib
Suggested calculator name: TRIG6 — you can give it another valid, unique name when you transfer it
Desktop test cases: Not available for this interactive-only source

This exact source auto-launches an interactive calculator session, so compatibility evidence comes from the recorded physical-device review rather than an importable desktop fixture.

Transfer and launch

Download the .py file, send it to your calculator with TI Connect CE as TRIG6 or another name, then open the Python App and try the worked example on this page first. This release has no verified calculator OS or Python App version; treat transfer and execution as unverified until independently tested.

Full installation and troubleshooting guide. Check your teacher's or exam's rules before using any program.

Version history

1.0.0 — current version, published 2026-10-31. Download this reviewed version

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