mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-11-30 16:31:08 +00:00
123 lines
3.8 KiB
Python
123 lines
3.8 KiB
Python
"""
|
|
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
|
|
: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)
|
|
-0.5440211108893691
|
|
>>> maclaurin_sin(-10)
|
|
0.5440211108893704
|
|
>>> maclaurin_sin(10, 15)
|
|
-0.544021110889369
|
|
>>> maclaurin_sin(-10, 15)
|
|
0.5440211108893704
|
|
>>> 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)
|
|
)
|
|
|
|
|
|
def maclaurin_cos(theta: float, accuracy: int = 30) -> float:
|
|
"""
|
|
Finds the maclaurin approximation of cos
|
|
|
|
:param theta: the angle to which cos is found
|
|
:param accuracy: the degree of accuracy wanted
|
|
:return: the value of cosine in radians
|
|
|
|
|
|
>>> from math import isclose, cos
|
|
>>> all(isclose(maclaurin_cos(x, 50), cos(x)) for x in range(-25, 25))
|
|
True
|
|
>>> maclaurin_cos(5)
|
|
0.2836621854632268
|
|
>>> maclaurin_cos(-5)
|
|
0.2836621854632265
|
|
>>> maclaurin_cos(10, 15)
|
|
-0.8390715290764524
|
|
>>> maclaurin_cos(-10, 15)
|
|
-0.8390715290764521
|
|
>>> maclaurin_cos("10")
|
|
Traceback (most recent call last):
|
|
...
|
|
ValueError: maclaurin_cos() requires either an int or float for theta
|
|
>>> maclaurin_cos(10, -30)
|
|
Traceback (most recent call last):
|
|
...
|
|
ValueError: maclaurin_cos() requires a positive int for accuracy
|
|
>>> maclaurin_cos(10, 30.5)
|
|
Traceback (most recent call last):
|
|
...
|
|
ValueError: maclaurin_cos() requires a positive int for accuracy
|
|
>>> maclaurin_cos(10, "30")
|
|
Traceback (most recent call last):
|
|
...
|
|
ValueError: maclaurin_cos() requires a positive int for accuracy
|
|
"""
|
|
|
|
if not isinstance(theta, (int, float)):
|
|
raise ValueError("maclaurin_cos() requires either an int or float for theta")
|
|
|
|
if not isinstance(accuracy, int) or accuracy <= 0:
|
|
raise ValueError("maclaurin_cos() requires a positive int for accuracy")
|
|
|
|
theta = float(theta)
|
|
div = theta // (2 * pi)
|
|
theta -= 2 * div * pi
|
|
return sum((-1) ** r * theta ** (2 * r) / factorial(2 * r) for r in range(accuracy))
|
|
|
|
|
|
if __name__ == "__main__":
|
|
import doctest
|
|
|
|
doctest.testmod()
|
|
|
|
print(maclaurin_sin(10))
|
|
print(maclaurin_sin(-10))
|
|
print(maclaurin_sin(10, 15))
|
|
print(maclaurin_sin(-10, 15))
|
|
|
|
print(maclaurin_cos(5))
|
|
print(maclaurin_cos(-5))
|
|
print(maclaurin_cos(10, 15))
|
|
print(maclaurin_cos(-10, 15))
|