mathdatech/Python
1
0
Fork 0
mirror of https://github.com/TheAlgorithms/Python.git synced 2024-11-23 21:11:08 +00:00
Code Issues Packages Projects Releases Wiki Activity

Maclaurin series approximation of sin (#7451)

Browse Source 
* added maclaurin_sin.py function

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* added type hints and fixed line overflows

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* removed incompatable type examples

* Update maths/maclaurin_sin.py

Co-authored-by: Caeden Perelli-Harris <caedenperelliharris@gmail.com>

* changed error details

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* fixed grammatical errors

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* improved function accuracy and added test case

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* Update maths/maclaurin_sin.py

Co-authored-by: Christian Clauss <cclauss@me.com>

* removed redundant return

* fixed pytest

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Co-authored-by: Caeden Perelli-Harris <caedenperelliharris@gmail.com>
Co-authored-by: Christian Clauss <cclauss@me.com>
This commit is contained in:
Chris O 2022-10-21 20:03:57 +13:00 committed by GitHub
parent 42b56f2345
commit 717f0e46d9
No known key found for this signature in database
GPG Key ID: 4AEE18F83AFDEB23
1 changed files with 64 additions and 0 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

64
maths/maclaurin_sin.py Normal file
View File

@ -0,0 +1,64 @@
"""
https://en.wikipedia.org/wiki/Taylor_series#Trigonometric_functions
"""
from math import factorial, pi
def maclaurin_sin(theta: float, accuracy: int = 30) -> float:
"""
Finds the maclaurin approximation of sin
:param theta: the angle to which sin is found
:param accuracy: the degree of accuracy wanted minimum ~ 1.5 theta
:return: the value of sine in radians
>>> from math import isclose, sin
>>> all(isclose(maclaurin_sin(x, 50), sin(x)) for x in range(-25, 25))
True
>>> maclaurin_sin(10)
-0.544021110889369
>>> maclaurin_sin(-10)
0.5440211108893703
>>> maclaurin_sin(10, 15)
-0.5440211108893689
>>> maclaurin_sin(-10, 15)
0.5440211108893703
>>> maclaurin_sin("10")
Traceback (most recent call last):
...
ValueError: maclaurin_sin() requires either an int or float for theta
>>> maclaurin_sin(10, -30)
Traceback (most recent call last):
...
ValueError: maclaurin_sin() requires a positive int for accuracy
>>> maclaurin_sin(10, 30.5)
Traceback (most recent call last):
...
ValueError: maclaurin_sin() requires a positive int for accuracy
>>> maclaurin_sin(10, "30")
Traceback (most recent call last):
...
ValueError: maclaurin_sin() requires a positive int for accuracy
"""
if not isinstance(theta, (int, float)):
raise ValueError("maclaurin_sin() requires either an int or float for theta")
if not isinstance(accuracy, int) or accuracy <= 0:
raise ValueError("maclaurin_sin() requires a positive int for accuracy")
theta = float(theta)
div = theta // (2 * pi)
theta -= 2 * div * pi
return sum(
(((-1) ** r) * ((theta ** (2 * r + 1)) / factorial(2 * r + 1)))
for r in range(accuracy)
)
if __name__ == "__main__":
print(maclaurin_sin(10))
print(maclaurin_sin(-10))
print(maclaurin_sin(10, 15))
print(maclaurin_sin(-10, 15))