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Maclaurin series approximation of sin (#7451)

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* added maclaurin_sin.py function

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* Update maths/maclaurin_sin.py

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

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* Update maths/maclaurin_sin.py

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