DuckieDai Quadrant from Trig Signs Python Program

trigonometry · MIT License

Overview

Find which quadrant an angle is in from the signs of two of its trig functions, such as sin positive and tan negative, with a sign chart and the All Students Take Calc rule.

Owner-tested on a TI calculator
Version 1.0.0
1999 bytes
No imports

Download QUADSIGN.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
csc has the same sign as sin, sec as cos, and cot as tan.
An angle on an axis is not in any quadrant.
Each sign is typed as 1 or + for positive and 2 or - for negative.

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Learn the math

How to find the quadrant from the signs of two trig functions

The idea

Each trig function is positive in two quadrants and negative in the other two. Knowing one sign leaves two possible quadrants; a second sign from a different pair usually narrows it to one.

Sine follows the y-coordinate and cosine follows the x-coordinate, so sine is positive above the x-axis and cosine is positive to the right of the y-axis. Tangent is sine over cosine, so it is positive where the two agree.

The formula

All Students Take Calc: Q I all, Q II sin, Q III tan, Q IV cos

csc has the sign of sin, sec the sign of cos, cot the sign of tan

Q I to Q IV: the four quadrants, numbered counterclockwise from the top right
positive, > 0: typed as 1 or +
negative, < 0: typed as 2 or -

Using the program

Choose 1 to find a quadrant. Pick the first function by number, 1 sin to 6 cot, then its sign: 1 or + for positive, 2 or - for negative.
Do the same for the second function.
The program shows ANSWER: QUADRANT and the quadrant, or the possible quadrants when the two signs do not settle it, or NO QUADRANT MATCHES.
Choose 2 to see the sign chart of sin, cos, and tan in every quadrant, with the All Students Take Calc rule.

Worked example

An angle has sin > 0 and tan < 0. Where does it end? Choose 1, then 1 for sin and 1 for positive, then 3 for tan and 2 for negative.

sin > 0: Q I or Q II; tan < 0: Q II or Q IV; both: Q II

The program shows sin > 0, tan < 0, and ANSWER: QUADRANT II.

With sin > 0 and csc > 0, both signs say the same thing, so the program shows POSSIBLE QUADRANTS: I, II and Need another sign.

Tips and common mistakes

Pick two functions from different pairs. sin and csc always share a sign, so together they tell you no more than one of them.
Remember which coordinate each function follows: sin with y, cos with x. That is quicker than memorizing a chart.
Signs that can never happen together, such as sin > 0 and csc < 0, mean a typo in the problem or the input.
An angle on an axis, such as 90 degrees, is in no quadrant; one of its values is 0 or undefined.

Where this comes up

Deciding the quadrant from signs is an early step in the trigonometric functions unit of precalculus, usually just before finding all six values from one.

Exact reviewed bytes

Source code

Download .py

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

# DuckieDai(TM) QUADSIGN
# TI-84 Plus CE Python Edition
# Find quadrants from TWO trig signs.

NAMES=('sin','cos','tan','csc','sec','cot')
IDX=(0,1,2,0,1,2)
SIGNS=((1,1,1),(1,-1,-1),(-1,-1,1),(-1,1,-1))
ROMAN=('I','II','III','IV')
PAD=('I  ','II ','III','IV ')

def clear():
 print('\n'*11)

def pause():
 input('Press enter ')
 clear()

def func():
 while True:
  print('1 sin  2 cos  3 tan')
  print('4 csc  5 sec  6 cot')
  try:
   n=int(input('Function? '))
   if 1<=n<=6:return n-1
  except ValueError:pass
  print('Choose 1-6')

def sign():
 while True:
  s=input('Sign? 1 +  2 - : ').strip().lower()
  if s in ('1','+','pos','positive','>0'):return 1
  if s in ('2','-','neg','negative','<0'):return -1
  print('Choose 1 or 2')

def label(f,s):
 return NAMES[f]+(' > 0' if s==1 else ' < 0')

def solve():
 clear()
 print('FIRST TRIG SIGN')
 a=func();sa=sign()
 clear()
 print('SECOND TRIG SIGN')
 b=func();sb=sign()
 hits=[]
 for q in range(4):
  if SIGNS[q][IDX[a]]==sa and SIGNS[q][IDX[b]]==sb:
   hits.append(ROMAN[q])
 clear()
 print(label(a,sa))
 print(label(b,sb))
 print('----------------')
 if len(hits)==1:
  print('ANSWER: QUADRANT '+hits[0])
 elif hits:
  print('POSSIBLE QUADRANTS:')
  print(', '.join(hits))
  print('Need another sign')
 else:
  print('NO QUADRANT MATCHES')
  print('Check the signs')
 pause()

def chart():
 clear()
 print('     sin cos tan')
 for q in range(4):
  signs=['+' if v==1 else '-' for v in SIGNS[q]]
  print(PAD[q]+':  '+'   '.join(signs))
 print('csc,sec,cot = sin,cos,tan')
 print('All Students Take Calc')
 print('I:All II:Sin III:Tan')
 print('IV:Cos')
 pause()

print('DuckieDai(TM)')
print('    QUADSIGN')
print('    __(o )>')
print('    \\ <_. ) QUACK!')
print("     `---'")
print('hiddenwordscanner.com')
pause()
while True:
 print('1 Find quadrant')
 print('2 Trig sign chart')
 print('3 Exit')
 c=input('Choice? ').strip()
 if c=='1':solve()
 elif c=='2':chart()
 elif c=='3':break
 else:print('Choose 1-3')
print('DuckieDai says: done!')

# DuckieDai(TM) QUADSIGN
# TI-84 Plus CE Python Edition
# Find quadrants from TWO trig signs.
NAMES=('sin','cos','tan','csc','sec','cot')
IDX=(0,1,2,0,1,2)
SIGNS=((1,1,1),(1,-1,-1),(-1,-1,1),(-1,1,-1))
ROMAN=('I','II','III','IV')
PAD=('I ','II ','III','IV ')
def clear():
print('\n'*11)
def pause():
input('Press enter ')
clear()
def func():
while True:
print('1 sin 2 cos 3 tan')
print('4 csc 5 sec 6 cot')
try:
n=int(input('Function? '))
if 1<=n<=6:return n-1
except ValueError:pass
print('Choose 1-6')
def sign():
while True:
s=input('Sign? 1 + 2 - : ').strip().lower()
if s in ('1','+','pos','positive','>0'):return 1
if s in ('2','-','neg','negative','<0'):return -1
print('Choose 1 or 2')
def label(f,s):
return NAMES[f]+(' > 0' if s==1 else ' < 0')
def solve():
clear()
print('FIRST TRIG SIGN')
a=func();sa=sign()
clear()
print('SECOND TRIG SIGN')
b=func();sb=sign()
hits=[]
for q in range(4):
if SIGNS[q][IDX[a]]==sa and SIGNS[q][IDX[b]]==sb:
hits.append(ROMAN[q])
clear()
print(label(a,sa))
print(label(b,sb))
print('----------------')
if len(hits)==1:
print('ANSWER: QUADRANT '+hits[0])
elif hits:
print('POSSIBLE QUADRANTS:')
print(', '.join(hits))
print('Need another sign')
else:
print('NO QUADRANT MATCHES')
print('Check the signs')
pause()
def chart():
clear()
print(' sin cos tan')
for q in range(4):
signs=['+' if v==1 else '-' for v in SIGNS[q]]
print(PAD[q]+': '+' '.join(signs))
print('csc,sec,cot = sin,cos,tan')
print('All Students Take Calc')
print('I:All II:Sin III:Tan')
print('IV:Cos')
pause()
print('DuckieDai(TM)')
print(' QUADSIGN')
print(' __(o )>')
print(' \\ <_. ) QUACK!')
print(" `---'")
print('hiddenwordscanner.com')
pause()
while True:
print('1 Find quadrant')
print('2 Trig sign chart')
print('3 Exit')
c=input('Choice? ').strip()
if c=='1':solve()
elif c=='2':chart()
elif c=='3':break
else:print('Choose 1-3')
print('DuckieDai says: done!')

Filename: QUADSIGN.py
Size: 1999 bytes
SHA-256: 5732159e45c6e7e40ab9ddfaad7a65c02e34a9974a343c5681a0cbfc88c3e9cc

Usage

Inputs

A menu choice: 1 find quadrant, 2 sign chart, 3 exit
Two trig functions, 1 sin to 6 cot, each with a sign

Outputs

ANSWER: QUADRANT and the quadrant, or the possible quadrants, or NO QUADRANT MATCHES
A chart of the signs of sin, cos, and tan in each quadrant

Units: Signs; no units.

Assumptions and limitations

Assumptions

csc has the same sign as sin, sec as cos, and cot as tan.
An angle on an axis is not in any quadrant.

Constraints

Each sign is typed as 1 or + for positive and 2 or - for negative.
Two signs of the same function, such as sin positive and csc positive, may leave two quadrants.

Known failures

Signs that cannot happen together, such as sin positive and csc negative, show NO QUADRANT MATCHES.

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 the sign chart's last lines were shortened so the chart fits on one calculator screen; nothing else changed. This exact file has not yet been rerun on a calculator.
Dependencies: No imports
Suggested calculator name: QUADSIGN — 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 QUADSIGN 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 2026-10-26. Download this reviewed version

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