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124 lines
3.8 KiB
Python
124 lines
3.8 KiB
Python
"""
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https://en.wikipedia.org/wiki/Taylor_series#Trigonometric_functions
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"""
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from math import factorial, pi
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def maclaurin_sin(theta: float, accuracy: int = 30) -> float:
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"""
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Finds the maclaurin approximation of sin
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:param theta: the angle to which sin is found
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:param accuracy: the degree of accuracy wanted minimum
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:return: the value of sine in radians
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>>> from math import isclose, sin
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>>> all(isclose(maclaurin_sin(x, 50), sin(x)) for x in range(-25, 25))
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True
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>>> maclaurin_sin(10)
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-0.5440211108893691
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>>> maclaurin_sin(-10)
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0.5440211108893704
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>>> maclaurin_sin(10, 15)
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-0.544021110889369
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>>> maclaurin_sin(-10, 15)
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0.5440211108893704
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>>> maclaurin_sin("10")
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Traceback (most recent call last):
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...
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ValueError: maclaurin_sin() requires either an int or float for theta
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>>> maclaurin_sin(10, -30)
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Traceback (most recent call last):
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...
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ValueError: maclaurin_sin() requires a positive int for accuracy
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>>> maclaurin_sin(10, 30.5)
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Traceback (most recent call last):
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...
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ValueError: maclaurin_sin() requires a positive int for accuracy
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>>> maclaurin_sin(10, "30")
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Traceback (most recent call last):
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...
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ValueError: maclaurin_sin() requires a positive int for accuracy
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"""
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if not isinstance(theta, (int, float)):
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raise ValueError("maclaurin_sin() requires either an int or float for theta")
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if not isinstance(accuracy, int) or accuracy <= 0:
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raise ValueError("maclaurin_sin() requires a positive int for accuracy")
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theta = float(theta)
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div = theta // (2 * pi)
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theta -= 2 * div * pi
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return sum(
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(-1) ** r * theta ** (2 * r + 1) / factorial(2 * r + 1) for r in range(accuracy)
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)
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def maclaurin_cos(theta: float, accuracy: int = 30) -> float:
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"""
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Finds the maclaurin approximation of cos
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:param theta: the angle to which cos is found
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:param accuracy: the degree of accuracy wanted
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:return: the value of cosine in radians
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>>> from math import isclose, cos
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>>> all(isclose(maclaurin_cos(x, 50), cos(x)) for x in range(-25, 25))
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True
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>>> maclaurin_cos(5)
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0.2836621854632268
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>>> maclaurin_cos(-5)
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0.2836621854632265
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>>> maclaurin_cos(10, 15)
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-0.8390715290764524
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>>> maclaurin_cos(-10, 15)
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-0.8390715290764521
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>>> maclaurin_cos("10")
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Traceback (most recent call last):
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...
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ValueError: maclaurin_cos() requires either an int or float for theta
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>>> maclaurin_cos(10, -30)
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Traceback (most recent call last):
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...
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ValueError: maclaurin_cos() requires a positive int for accuracy
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>>> maclaurin_cos(10, 30.5)
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Traceback (most recent call last):
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...
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ValueError: maclaurin_cos() requires a positive int for accuracy
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>>> maclaurin_cos(10, "30")
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Traceback (most recent call last):
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...
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ValueError: maclaurin_cos() requires a positive int for accuracy
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"""
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if not isinstance(theta, (int, float)):
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raise ValueError("maclaurin_cos() requires either an int or float for theta")
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if not isinstance(accuracy, int) or accuracy <= 0:
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raise ValueError("maclaurin_cos() requires a positive int for accuracy")
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theta = float(theta)
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div = theta // (2 * pi)
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theta -= 2 * div * pi
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return sum((-1) ** r * theta ** (2 * r) / factorial(2 * r) for r in range(accuracy))
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if __name__ == "__main__":
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import doctest
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doctest.testmod()
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print(maclaurin_sin(10))
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print(maclaurin_sin(-10))
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print(maclaurin_sin(10, 15))
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print(maclaurin_sin(-10, 15))
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print(maclaurin_cos(5))
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print(maclaurin_cos(-5))
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print(maclaurin_cos(10, 15))
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print(maclaurin_cos(-10, 15))
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