maclaurin_sin.py

"""
https://en.wikipedia.org/wiki/Taylor_series#Trigonometric_functions
"""
from math import factorial


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

    >>> maclaurin_sin(10)
    -0.54402111088927
    >>> maclaurin_sin(-10)
    0.54402111088927
    >>> maclaurin_sin(10, 15)
    -0.5429111519640644
    >>> maclaurin_sin(-10, 15)
    0.5429111519640644
    >>> 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)

    total = 0
    for r in range(accuracy):
        total += ((-1) ** r) * ((theta ** (2 * r + 1)) / (factorial(2 * r + 1)))
    return float(total)


if __name__ == "__main__":
    print(maclaurin_sin(10, 15))