#### Maclaurin Series

p
```"""
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))
```