Maclaurin series approximation of sin (#7451)

* added maclaurin_sin.py function

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* removed incompatable type examples

* Update maths/maclaurin_sin.py

Co-authored-by: Caeden Perelli-Harris <[email protected]>

* changed error details

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* fixed grammatical errors

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* improved function accuracy and added test case

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* Update maths/maclaurin_sin.py

Co-authored-by: Christian Clauss <[email protected]>

* removed redundant return

* fixed pytest

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Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Co-authored-by: Caeden Perelli-Harris <[email protected]>
Co-authored-by: Christian Clauss <[email protected]>

Author: 4 people

maths/maclaurin_sin.py

@@ -0,0 +1,64 @@
+"""
+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))