






from math import factorial, pi



def 			_SCREAMING_SNAKE_CASE						( __lowercase   :			float			,				__lowercase   :			int = 3_0    )						->      float:





    """simple docstring"""

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

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

    __A         =	float(__lowercase    )
    __A         =	theta // (2 * pi)
    theta -= 2 * div * pi
    return sum(
        (-1) ** r * theta ** (2 * r + 1) / factorial(2 * r + 1    ) for r in range(__lowercase    )    )



def 			_SCREAMING_SNAKE_CASE						( __lowercase   :			float			,				__lowercase   :			int = 3_0    )						->      float:





    """simple docstring"""

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

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

    __A         =	float(__lowercase    )
    __A         =	theta // (2 * pi)
    theta -= 2 * div * pi
    return sum((-1) ** r * theta ** (2 * r) / factorial(2 * r    ) for r in range(__lowercase    )    )


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))












__a      :       List[Any]				  =   8.3_1_4_4_5_9_8



def 			_SCREAMING_SNAKE_CASE						( __lowercase   :			float			,				__lowercase   :			float    )						->      float:





    """simple docstring"""

    if temperature < 0:
        raise Exception("""Temperature cannot be less than 0 K"""    )
    if molar_mass <= 0:
        raise Exception("""Molar mass cannot be less than or equal to 0 kg/mol"""    )
    else:
        return (3 * UNIVERSAL_GAS_CONSTANT * temperature / molar_mass) ** 0.5


if __name__ == "__main__":
  import doctest

  # run doctest
  doctest.testmod()

  # example
  __a      :       int				  =   300
  __a      :       int				  =   28
  __a      :       int				  =   rms_speed_of_molecule(temperature, molar_mass)
  print(f"""Vrms of Nitrogen gas at 300 K is {vrms} m/s""")




