Add sin function to maths (#5949)

* Add sin function to /maths.

* Fix typo in /maths/sin.py

* Format sin.py to meet the new black rules.

* Some improvements.

* Fix a formating error.

maths/sin.py

@@ -0,0 +1,64 @@
+"""
+Calculate sin function.
+
+It's not a perfect function so I am rounding the result to 10 decimal places by default.
+
+Formula: sin(x) = x - x^3/3! + x^5/5! - x^7/7! + ...
+Where: x = angle in randians.
+
+Source:
+    https://www.homeschoolmath.net/teaching/sine_calculator.php
+
+"""
+
+from math import factorial, radians
+
+
+def sin(
+    angle_in_degrees: float, accuracy: int = 18, rounded_values_count: int = 10
+) -> float:
+    """
+    Implement sin function.
+
+    >>> sin(0.0)
+    0.0
+    >>> sin(90.0)
+    1.0
+    >>> sin(180.0)
+    0.0
+    >>> sin(270.0)
+    -1.0
+    >>> sin(0.68)
+    0.0118679603
+    >>> sin(1.97)
+    0.0343762121
+    >>> sin(64.0)
+    0.8987940463
+    >>> sin(9999.0)
+    -0.9876883406
+    >>> sin(-689.0)
+    0.5150380749
+    >>> sin(89.7)
+    0.9999862922
+    """
+    # Simplify the angle to be between 360 and -360 degrees.
+    angle_in_degrees = angle_in_degrees - ((angle_in_degrees // 360.0) * 360.0)
+
+    # Converting from degrees to radians
+    angle_in_radians = radians(angle_in_degrees)
+
+    result = angle_in_radians
+    a = 3
+    b = -1
+
+    for _ in range(accuracy):
+        result += (b * (angle_in_radians**a)) / factorial(a)
+
+        b = -b  # One positive term and the next will be negative and so on...
+        a += 2  # Increased by 2 for every term.
+
+    return round(result, rounded_values_count)
+
+
+if __name__ == "__main__":
+    __import__("doctest").testmod()