DuckieDai Quick Trig Values Python Program

trigonometry · MIT License

Overview

Type a function and an angle, such as sin pi/4, and get its exact value, or type just an angle to see all six exact values.

Owner-tested on a TI calculator
Version 1.0.0
1628 bytes
Uses math

Download TRIGV.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
An angle without pi is read as degrees.
Exact values are given for multiples of 30 and 45 degrees.
Function names are sin, cos, tan, csc, sec, and cot.

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Follow the program's prompts and result flow before downloading.

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Learn the math

How to look up exact trig values quickly

The idea

Trig values of the standard angles, the multiples of 30 and 45 degrees, come up so often that it pays to know them by sight. Each one is built from a special right triangle and a sign that depends on where the angle ends.

This program is the quick version: type the function and the angle on one line, the way you would read it aloud, and the exact value appears. Type just an angle to see all six values at once.

The formula

sin^2 + cos^2 = 1

tan = sin/cos

csc = 1/sin, sec = 1/cos, cot = 1/tan

pi: a half turn, 180 degrees
undefined: a value with 0 on the bottom, such as tan 90
exact value: a fraction with square roots, such as sqrt(3)/2, in place of a rounded decimal

Using the program

Type a function and an angle, such as sin pi/4, tan(pi/2), or cos 60. Spaces and parentheses are optional.
Type only an angle, such as pi/6, to see all six values; press Enter after the first three to see the rest.
An angle without pi is in degrees. A pi angle is a fraction such as 5pi/6.
For an angle that is not standard, the program shows sin, cos, and tan as decimals to four places.
Press Enter with nothing typed to quit.

Worked example

Type sin 5pi/6. The angle is 150 degrees, in Quadrant 2, with a reference angle of 30 degrees, where sine is positive.

sin 150 = sin 30 = 1/2

The program shows Angle = 150 deg and sin = 1/2.

Type pi/4 for all six values. The program shows sin = sqrt(2)/2, cos = sqrt(2)/2, and tan = 1, then csc = sqrt(2), sec = sqrt(2), and cot = 1.

Type tan 90. Cosine is 0 at 90 degrees, so the program shows tan = undefined. Type 20, which is not a standard angle, and the program shows sin = 0.342, cos = 0.9397, and tan = 0.364.

Tips and common mistakes

Check a value by squaring: sin^2 + cos^2 must equal 1. For pi/4, (sqrt(2)/2)^2 + (sqrt(2)/2)^2 = 1/2 + 1/2 = 1.
csc, sec, and cot are reciprocals, not inverses: csc 30 = 2, while the inverse sine of 1/2 is 30 degrees.
Decimals such as 0.342 are rounded; keep the exact value when a question asks for one.
If the program says Bad angle, check for a typing slip such as pi/0 or a missing number.

Where this comes up

Exact values of the standard angles are used throughout precalculus, physics vector problems, and calculus, wherever a sine or cosine of 30, 45, or 60 degrees appears.

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
def clr():print("\n"*11)
def pg():input("[enter]");clr()
def fmt(x):
 r=round(x)
 return str(int(r)) if abs(x-r)<1e-9 else str(round(x,4))
def gcd(a,b):
 while b:a,b=b,a%b
 return a
def ex(p,q):
 g=gcd(p,q);p//=g;q//=g;n=p*q;k=1;d=2
 while d*d<=n:
  if n%(d*d):d+=1
  else:n//=d*d;k*=d
 g=gcd(k,q);k//=g;q//=g
 s=str(k) if n==1 else ("" if k==1 else str(k))+"sqrt("+str(n)+")"
 return s if q==1 else s+"/"+str(q)
def sg(x):return (x>1e-9)-(x<-1e-9)
def e(p,q,s):
 if q==0:return "undefined"
 if s==0:return "0"
 return ("-" if s<0 else "")+ex(p,q)
def go(s):
 s=s.replace("π","pi").replace("*","").replace(" ","");f=""
 for n in N:
  if s.startswith(n):f=n;s=s[3:].strip("()")
 try:
  if "pi" in s:
   a,b=(s+"/1").split("/")[:2];a=a.replace("pi","")
   t=float(a+"1" if a in("","-") else a)*180/float(b)
  else:t=float(s)
  if t-t:raise ValueError
 except (ValueError,ZeroDivisionError):print("Bad angle");return
 t%=360;x=t*pi/180;r=t%180;r=min(r,180-r);clr()
 print("Angle =",fmt(t),"deg");S=sg(sin(x));C=sg(cos(x))
 v=None
 if abs(r-round(r))<1e-6:v={0:(0,1),30:(1,4),45:(1,2),60:(3,4),90:(1,1)}.get(round(r))
 if not v:print("sin =",fmt(sin(x)));print("cos =",fmt(cos(x)));print("tan =",fmt(sin(x)/cos(x)));pg();return
 p,q=v;c=q-p
 L=[e(p,q,S),e(c,q,C),e(p,c,S*C),e(q,p,S),e(q,c,C),e(c,p,S*C)]
 for i in range(6):
  if f in("",N[i]):print(N[i],"=",L[i])
  if i==2 and not f:pg()
 pg()
N=["sin","cos","tan","csc","sec","cot"]
clr();print("TRIG VALUES - DuckieDai\nhiddenwordscanner.com\nType: sin pi/4  or  pi/6\nBlank entry = quit")
while 1:
 s=input("Angle? ").strip()
 if not s:break
 go(s)

from math import sin,cos,pi
def clr():print("\n"*11)
def pg():input("[enter]");clr()
def fmt(x):
r=round(x)
return str(int(r)) if abs(x-r)<1e-9 else str(round(x,4))
def gcd(a,b):
while b:a,b=b,a%b
return a
def ex(p,q):
g=gcd(p,q);p//=g;q//=g;n=p*q;k=1;d=2
while d*d<=n:
if n%(d*d):d+=1
else:n//=d*d;k*=d
g=gcd(k,q);k//=g;q//=g
s=str(k) if n==1 else ("" if k==1 else str(k))+"sqrt("+str(n)+")"
return s if q==1 else s+"/"+str(q)
def sg(x):return (x>1e-9)-(x<-1e-9)
def e(p,q,s):
if q==0:return "undefined"
if s==0:return "0"
return ("-" if s<0 else "")+ex(p,q)
def go(s):
s=s.replace("π","pi").replace("*","").replace(" ","");f=""
for n in N:
if s.startswith(n):f=n;s=s[3:].strip("()")
try:
if "pi" in s:
a,b=(s+"/1").split("/")[:2];a=a.replace("pi","")
t=float(a+"1" if a in("","-") else a)*180/float(b)
else:t=float(s)
if t-t:raise ValueError
except (ValueError,ZeroDivisionError):print("Bad angle");return
t%=360;x=t*pi/180;r=t%180;r=min(r,180-r);clr()
print("Angle =",fmt(t),"deg");S=sg(sin(x));C=sg(cos(x))
v=None
if abs(r-round(r))<1e-6:v={0:(0,1),30:(1,4),45:(1,2),60:(3,4),90:(1,1)}.get(round(r))
if not v:print("sin =",fmt(sin(x)));print("cos =",fmt(cos(x)));print("tan =",fmt(sin(x)/cos(x)));pg();return
p,q=v;c=q-p
L=[e(p,q,S),e(c,q,C),e(p,c,S*C),e(q,p,S),e(q,c,C),e(c,p,S*C)]
for i in range(6):
if f in("",N[i]):print(N[i],"=",L[i])
if i==2 and not f:pg()
pg()
N=["sin","cos","tan","csc","sec","cot"]
clr();print("TRIG VALUES - DuckieDai\nhiddenwordscanner.com\nType: sin pi/4 or pi/6\nBlank entry = quit")
while 1:
s=input("Angle? ").strip()
if not s:break
go(s)

Filename: TRIGV.py
Size: 1628 bytes
SHA-256: eb5cca5052305e5734caa793ddf05dadae319e533768067862562eeb9d259d83

Usage

Inputs

An angle, such as 30 or pi/6, optionally after a function name, such as sin pi/4 or tan(pi/2)
Enter with nothing typed to quit

Outputs

The angle in degrees from 0 up to 360
The exact value of the function asked for, or all six, such as sqrt(3)/2 or undefined
For other angles, sin, cos, and tan as decimals to four places

Units: Angles in degrees or as a multiple of pi.

Assumptions and limitations

Assumptions

An angle without pi is read as degrees.
Exact values are given for multiples of 30 and 45 degrees.

Constraints

Function names are sin, cos, tan, csc, sec, and cot.
A pi angle is typed as a fraction such as 5pi/6; inf and nan show Bad angle.

Known failures

For an angle that is not standard, the program shows sin, cos, and tan as decimals even when one function was asked for.

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 two changes: the website line was added to the opening screen, and inf or nan typed as an angle now shows Bad angle, where the original stopped with an error. Every other step is unchanged; this exact file has not yet been rerun on a calculator.
Dependencies: math
Suggested calculator name: TRIGV — 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 TRIGV 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 2026-10-22. Download this reviewed version

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