


from math import factorial, pi





def 	_lowerCAmelCase					( 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"""    )

	A             =					float(UpperCamelCase__    )
	A             =					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 	_lowerCAmelCase					( 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"""    )

	A             =					float(UpperCamelCase__    )
	A             =					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))







_lowercase							:   Dict						=						{
    "Pillow": "Pillow",
    "accelerate": "accelerate>=0.11.0",
    "compel": "compel==0.1.8",
    "black": "black~=23.1",
    "datasets": "datasets",
    "filelock": "filelock",
    "flax": "flax>=0.4.1",
    "hf-doc-builder": "hf-doc-builder>=0.3.0",
    "huggingface-hub": "huggingface-hub>=0.13.2",
    "requests-mock": "requests-mock==1.10.0",
    "importlib_metadata": "importlib_metadata",
    "invisible-watermark": "invisible-watermark",
    "isort": "isort>=5.5.4",
    "jax": "jax>=0.2.8,!=0.3.2",
    "jaxlib": "jaxlib>=0.1.65",
    "Jinja2": "Jinja2",
    "k-diffusion": "k-diffusion>=0.0.12",
    "torchsde": "torchsde",
    "note_seq": "note_seq",
    "librosa": "librosa",
    "numpy": "numpy",
    "omegaconf": "omegaconf",
    "parameterized": "parameterized",
    "protobuf": "protobuf>=3.20.3,<4",
    "pytest": "pytest",
    "pytest-timeout": "pytest-timeout",
    "pytest-xdist": "pytest-xdist",
    "ruff": "ruff>=0.0.241",
    "safetensors": "safetensors",
    "sentencepiece": "sentencepiece>=0.1.91,!=0.1.92",
    "scipy": "scipy",
    "onnx": "onnx",
    "regex": "regex!=2019.12.17",
    "requests": "requests",
    "tensorboard": "tensorboard",
    "torch": "torch>=1.4",
    "torchvision": "torchvision",
    "transformers": "transformers>=4.25.1",
    "urllib3": "urllib3<=2.0.0",
}



