



from __future__ import annotations






def      _A				(UpperCamelCase		:      List[str] )  ->list[int]:



			'''simple docstring'''







			lowerCamelCase__ :      Union[str, Any]								=		2
			lowerCamelCase__ :      Union[str, Any]								=		[]
			while i * i <= n:
						if n % i:
									i += 1
						else:
									n //= i
									factors.append(_SCREAMING_SNAKE_CASE )
			if n > 1:
						factors.append(_SCREAMING_SNAKE_CASE )
			return factors


if __name__ == "__main__":
				import doctest

				doctest.testmod()








from math import factorial, pi






def      _A				(UpperCamelCase		:      float      ,			UpperCamelCase		:      int = 30 )  ->float:



			'''simple docstring'''







			if not isinstance(UpperCamelCase      ,			(int, float) ):
						raise ValueError("""maclaurin_sin() requires either an int or float for theta""" )

			if not isinstance(UpperCamelCase      ,			UpperCamelCase ) or accuracy <= 0:
						raise ValueError("""maclaurin_sin() requires a positive int for accuracy""" )

			lowerCamelCase__ :      Dict								=		float(UpperCamelCase )
			lowerCamelCase__ :      int								=		theta // (2 * pi)
			theta -= 2 * div * pi
			return sum(
			    (-1) ** r * theta ** (2 * r + 1) / factorial(2 * r + 1 ) for r in range(UpperCamelCase ) )






def      _A				(UpperCamelCase		:      float      ,			UpperCamelCase		:      int = 30 )  ->float:



			'''simple docstring'''







			if not isinstance(UpperCamelCase      ,			(int, float) ):
						raise ValueError("""maclaurin_cos() requires either an int or float for theta""" )

			if not isinstance(UpperCamelCase      ,			UpperCamelCase ) or accuracy <= 0:
						raise ValueError("""maclaurin_cos() requires a positive int for accuracy""" )

			lowerCamelCase__ :      int								=		float(UpperCamelCase )
			lowerCamelCase__ :      Optional[int]								=		theta // (2 * pi)
			theta -= 2 * div * pi
			return sum((-1) ** r * theta ** (2 * r) / factorial(2 * r ) for r in range(UpperCamelCase ) )


if __name__ == "__main__":
				import doctest

				doctest.testmod()

				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))



