From a5dd07c3707a0d3ebde0321ce7984082b3d322ff Mon Sep 17 00:00:00 2001
From: Chris O <46587501+ChrisO345@users.noreply.github.com>
Date: Sun, 23 Oct 2022 05:17:07 +1300
Subject: [PATCH] Maclaurin approximation of cos (#7507)

* renamed maclaurin_sin.py to maclaurin_series.py and included function for cos approximation

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* attempt to fix pytest error

Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
---
 maths/maclaurin_series.py | 121 ++++++++++++++++++++++++++++++++++++++
 maths/maclaurin_sin.py    |  64 --------------------
 2 files changed, 121 insertions(+), 64 deletions(-)
 create mode 100644 maths/maclaurin_series.py
 delete mode 100644 maths/maclaurin_sin.py

diff --git a/maths/maclaurin_series.py b/maths/maclaurin_series.py
new file mode 100644
index 000000000..57edc90bf
--- /dev/null
+++ b/maths/maclaurin_series.py
@@ -0,0 +1,121 @@
+"""
+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)
+    -0.544021110889369
+    >>> 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)
+    )
+
+
+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)
+    0.28366218546322675
+    >>> maclaurin_cos(-5)
+    0.2836621854632266
+    >>> maclaurin_cos(10, 15)
+    -0.8390715290764525
+    >>> 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__":
+    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))
diff --git a/maths/maclaurin_sin.py b/maths/maclaurin_sin.py
deleted file mode 100644
index 3c27ccf63..000000000
--- a/maths/maclaurin_sin.py
+++ /dev/null
@@ -1,64 +0,0 @@
-"""
-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))