DuckieDai Trig Tools Python Program

trigonometry · MIT License

Overview

Four angle tools in one program: find coterminal angles, change degrees to radians, change a multiple of pi to degrees, and name an angle's quadrant and type.

Owner-tested on a TI calculator
Version 1.0.0
2896 bytes
Uses math

Download TRIGMAIN.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
Angles are measured from the positive x-axis, counterclockwise for positive angles.
For Angle/quad, the angle is first reduced to one turn, 0 up to 360 degrees, and the answer describes that angle.
Numbers may be typed as decimals or fractions such as 1/3; inf and nan are asked for again.

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Learn the math

How coterminal angles, radians, and quadrants work

The idea

An angle in standard position starts on the positive x-axis and turns, counterclockwise for a positive angle and clockwise for a negative one. Turning a full circle, 360 degrees or 2pi radians, lands you back where you began.

So angles that differ by whole turns end in the same place. They are called coterminal, and every angle has one between 0 and 360 degrees. Where an angle ends decides its quadrant, and that decides the signs of sine, cosine, and tangent.

The formula

coterminal angle = angle + 360k (k any whole number)

radians = degrees*pi/180

degrees = (multiple of pi)*180

360 or 2pi: one full turn, in degrees or radians
k: how many whole turns are added or taken away
Quadrant 1 to 4: the four regions between the axes, numbered counterclockwise from the top right

Using the program

Choose 1 for coterminal angles, then give the angle in degrees, as a fraction of pi such as 3/4 for 3pi/4, or in radians. The program shows the coterminal angle from just above 0 up to one full turn, and the matching negative angle.
Choose 2 to change degrees to radians. Whole-number degrees also get an EXACT answer as a fraction times pi.
Choose 3 to change a multiple of pi to degrees: type 1/3 for pi/3.
Choose 4 to find where an angle ends. The program names the quadrant and its direction, such as Up-left, or the axis it lies on, then says whether the angle is acute, right, obtuse, straight, or reflex.
Numbers can be decimals or fractions such as 1/3.

Worked example

Find a positive and a negative angle coterminal with -30 degrees. Choose 1, then 1 for degrees, and enter -30.

-30 + 360 = 330, 330 - 360 = -30

The program shows Positive: 330.0 and Negative: -30.0.

For 17pi/6, choose 1, then 2, and type 17/6. Taking away one full turn, 12pi/6, leaves 5pi/6, so the program shows Positive: 5/6pi and Negative: -7/6pi.

Change 90 degrees to radians: choose 2 and enter 90. The program shows EXACT: 1/2 pi and DEC: 1.570796.

Where does 135 degrees end? Choose 4, then 1, and enter 135. The program shows Quadrant 2, Up-left, and Obtuse.

Tips and common mistakes

Every angle has endless coterminal angles. The program gives the one in the first full turn and the negative one next to it; add or subtract 360 for more.
A full turn counts as 360 degrees, or 2pi, as the positive angle, and -360 degrees, or -2pi, as the negative one.
For Angle/quad, a negative or larger angle is first brought into 0 to 360 degrees, so -30 is described as 330: Quadrant 4 and reflex.
Remember ASTC for the quadrants: All three trig functions are positive in Quadrant 1, Sine in 2, Tangent in 3, and Cosine in 4.

Where this comes up

Coterminal angles, radian measure, and quadrants open the trigonometry unit in precalculus and algebra 2, and they come back whenever the unit circle is used.

Exact reviewed bytes

Source code

Download .py

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

# DUCKIEDAI TM - TRIG LITE
# TI-84 CE PYTHON
from math import pi

def n(p):
 while 1:
  try:
   s=input(p)
   if '/' in s:
    a,b=s.split('/')
    v=float(a)/float(b)
   else:v=float(s)
   if v-v:raise ValueError
   return v
  except:
   print('Try again')

def f(a,b):
 a=int(a);b=int(b)
 x=abs(a);y=abs(b)
 while y:x,y=y,x%y
 if x:a//=x;b//=x
 if b==1:return str(a)
 return str(a)+'/'+str(b)

def pause():
 input("ENTER to continue")

def intro():
 print('DUCKIEDAI(TM)')
 print('TRIG TOOLS')
 print('      __')
 print('  ___(o )> quack!')
 print('  \\ <_. )')
 print("   `---'")
 print('by DuckieDai')
 print('hiddenwordscanner.com')
 input('Press Enter ')
 print('\n'*7)

def bye():
 print('DUCKIEDAI (TM)')
 print('hiddenwordscanner.com')
 input('ENTER to exit')

def menu():
 while 1:
  print('\n'*8)
  print('DUCKIEDAI TM TRIG')
  print('1 Coterminal')
  print('2 Deg to rad')
  print('3 pi to deg')
  print('4 Angle/quad')
  print('0 Exit')
  k=input('Pick: ')
  if k=='0':break
  if k=='1':
   print('1 Deg 2 Pi 3 Rad')
   z=input('Angle type: ')
   if z=='1':
    a=n('Degrees: ')
    v=a%360
    print('Positive:',v if v else 360)
    print('Negative:',v-360 if v else -360)
   elif z=='2':
    try:
     s=input('Pi fraction (a/b): ')
     if '/' in s:
      x,y=s.split('/')
      a=int(x);b=int(y)
     else:
      a=int(s);b=1
     if b==0:raise ValueError
     if b<0:a=-a;b=-b
     v=a%(2*b);w=v-2*b
     if v==0:v=2*b
     print('Positive:',f(v,b)+'pi')
     print('Negative:',f(w,b)+'pi')
    except:
     print('Invalid fraction')
   elif z=='3':
    a=n('Radians: ')
    v=a%(2*pi)
    if abs(v)<1e-9 or abs(v-2*pi)<1e-9:v=0
    print('Positive:',round(v if v else 2*pi,6))
    print('Negative:',round(v-2*pi,6))
   else:print('Invalid type')
  elif k=='2':
   a=n('Degrees: ')
   if a==int(a):
    print('EXACT:',f(a,180),'pi')
   print('DEC:',round(a*pi/180,6))
  elif k=='3':
   print('Enter coefficient of pi')
   a=n('pi x: ')
   print('Degrees:',round(a*180,6))
  elif k=='4':
   print('1 Deg 2 Pi 3 Rad')
   z=input('Angle type: ')
   if z=='1':
    a=n('Degrees: ')%360
   elif z=='2':
    a=(n('Pi coefficient: ')*2)%4
    a=a*90
   elif z=='3':
    a=(n('Radians: ')%(2*pi))*180/pi
   else:
    print('Invalid type')
    pause()
    continue
   if abs(a-360)<1e-8:a=0
   if abs(a)<1e-8:print('+X axis')
   elif abs(a-90)<1e-8:print('+Y axis')
   elif abs(a-180)<1e-8:print('-X axis')
   elif abs(a-270)<1e-8:print('-Y axis')
   else:
    q=int(a//90)+1
    print('Quadrant',q)
    if q==1:print('Up-right')
    elif q==2:print('Up-left')
    elif q==3:print('Down-left')
    else:print('Down-right')
   if abs(a-90)<1e-8:print('Right')
   elif abs(a-180)<1e-8:print('Straight')
   elif abs(a)<1e-8:print('Zero/full')
   elif a<90:print('Acute')
   elif a<180:print('Obtuse')
   else:print('Reflex')
  else:print('Try 0-4')
  if k!='0':pause()
intro()
menu()
bye()

# DUCKIEDAI TM - TRIG LITE
# TI-84 CE PYTHON
from math import pi
def n(p):
while 1:
try:
s=input(p)
if '/' in s:
a,b=s.split('/')
v=float(a)/float(b)
else:v=float(s)
if v-v:raise ValueError
return v
except:
print('Try again')
def f(a,b):
a=int(a);b=int(b)
x=abs(a);y=abs(b)
while y:x,y=y,x%y
if x:a//=x;b//=x
if b==1:return str(a)
return str(a)+'/'+str(b)
def pause():
input("ENTER to continue")
def intro():
print('DUCKIEDAI(TM)')
print('TRIG TOOLS')
print(' __')
print(' ___(o )> quack!')
print(' \\ <_. )')
print(" `---'")
print('by DuckieDai')
print('hiddenwordscanner.com')
input('Press Enter ')
print('\n'*7)
def bye():
print('DUCKIEDAI (TM)')
print('hiddenwordscanner.com')
input('ENTER to exit')
def menu():
while 1:
print('\n'*8)
print('DUCKIEDAI TM TRIG')
print('1 Coterminal')
print('2 Deg to rad')
print('3 pi to deg')
print('4 Angle/quad')
print('0 Exit')
k=input('Pick: ')
if k=='0':break
if k=='1':
print('1 Deg 2 Pi 3 Rad')
z=input('Angle type: ')
if z=='1':
a=n('Degrees: ')
v=a%360
print('Positive:',v if v else 360)
print('Negative:',v-360 if v else -360)
elif z=='2':
try:
s=input('Pi fraction (a/b): ')
if '/' in s:
x,y=s.split('/')
a=int(x);b=int(y)
else:
a=int(s);b=1
if b==0:raise ValueError
if b<0:a=-a;b=-b
v=a%(2*b);w=v-2*b
if v==0:v=2*b
print('Positive:',f(v,b)+'pi')
print('Negative:',f(w,b)+'pi')
except:
print('Invalid fraction')
elif z=='3':
a=n('Radians: ')
v=a%(2*pi)
if abs(v)<1e-9 or abs(v-2*pi)<1e-9:v=0
print('Positive:',round(v if v else 2*pi,6))
print('Negative:',round(v-2*pi,6))
else:print('Invalid type')
elif k=='2':
a=n('Degrees: ')
if a==int(a):
print('EXACT:',f(a,180),'pi')
print('DEC:',round(a*pi/180,6))
elif k=='3':
print('Enter coefficient of pi')
a=n('pi x: ')
print('Degrees:',round(a*180,6))
elif k=='4':
print('1 Deg 2 Pi 3 Rad')
z=input('Angle type: ')
if z=='1':
a=n('Degrees: ')%360
elif z=='2':
a=(n('Pi coefficient: ')*2)%4
a=a*90
elif z=='3':
a=(n('Radians: ')%(2*pi))*180/pi
else:
print('Invalid type')
pause()
continue
if abs(a-360)<1e-8:a=0
if abs(a)<1e-8:print('+X axis')
elif abs(a-90)<1e-8:print('+Y axis')
elif abs(a-180)<1e-8:print('-X axis')
elif abs(a-270)<1e-8:print('-Y axis')
else:
q=int(a//90)+1
print('Quadrant',q)
if q==1:print('Up-right')
elif q==2:print('Up-left')
elif q==3:print('Down-left')
else:print('Down-right')
if abs(a-90)<1e-8:print('Right')
elif abs(a-180)<1e-8:print('Straight')
elif abs(a)<1e-8:print('Zero/full')
elif a<90:print('Acute')
elif a<180:print('Obtuse')
else:print('Reflex')
else:print('Try 0-4')
if k!='0':pause()
intro()
menu()
bye()

Filename: TRIGMAIN.py
Size: 2896 bytes
SHA-256: 82f18c0baff941d55f24c7f51b184cbb074a62b44e431a4c389838c631b8ff79

Usage

Inputs

A menu choice: 1 coterminal angles, 2 degrees to radians, 3 a multiple of pi to degrees, 4 quadrant and angle type
An angle in degrees, as a fraction or multiple of pi, or in radians

Outputs

A positive and a negative coterminal angle in the same form as the input
Radians exactly in terms of pi and as a decimal, or degrees from a multiple of pi
The quadrant or axis of an angle, and whether it is acute, right, obtuse, straight, or reflex

Units: Angles in degrees, multiples of pi, or radians.

Assumptions and limitations

Assumptions

Angles are measured from the positive x-axis, counterclockwise for positive angles.
For Angle/quad, the angle is first reduced to one turn, 0 up to 360 degrees, and the answer describes that angle.

Constraints

Numbers may be typed as decimals or fractions such as 1/3; inf and nan are asked for again.
A pi fraction for coterminal angles must be whole numbers, such as 3/4 for 3pi/4.
Degrees to radians shows an exact answer in terms of pi only for whole-number degrees.

Known failures

Coterminal angles in degrees are not rounded, so 1/3 shows every digit Python prints.
Angles within about 0.00000001 degree of an axis are reported as on that axis.

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 before three fixes: the number prompt now asks again when inf or nan is typed, where the original stopped with an error, and a full turn now shows 2pi and 6.283185 as its negative coterminal angle in place of 0pi and 0.0. Every other step is unchanged; this exact file has not yet been rerun on a calculator.
Dependencies: math
Suggested calculator name: TRIGMAIN — 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 TRIGMAIN 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 2026-10-13. Download this reviewed version

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