import math




def    lowerCAmelCase_  (		lowercase:				float	,       lowercase:				float		)     ->					float:







 '''simple docstring'''

 if initial_intensity < 0:
  raise ValueError('''The value of intensity cannot be negative'''		)
  # handling of negative values of initial intensity
 if angle < 0 or angle > 360:
  raise ValueError('''In Malus Law, the angle is in the range 0-360 degrees'''		)
  # handling of values out of allowed range
 return initial_intensity * (math.cos(math.radians(lowercase		)		) ** 2)


if __name__ == "__main__":
  import doctest

  doctest.testmod(name='''malus_law''')
from sympy import diff, lambdify, symbols
from sympy.functions import *  # noqa: F403




def    lowerCAmelCase_  (		lowercase:				str	,       lowercase:				complex	,       lowercase:				str = "x"	,       lowercase:				float = 10**-10	,       lowercase:				int = 1	,       )     ->					complex:







 '''simple docstring'''
 _UpperCamelCase:  Any    						=			symbols(lowercase		)
 _UpperCamelCase:  str    						=			lambdify(lowercase	,       lowercase		)
 _UpperCamelCase:  str    						=			lambdify(lowercase	,       diff(lowercase	,       lowercase		)		)

 _UpperCamelCase:  Optional[int]    						=			starting_point

 while True:
  if diff_function(lowercase		) != 0:
   _UpperCamelCase:  int    						=			prev_guess - multiplicity * func(lowercase		) / diff_function(
       lowercase		)
  else:
   raise ZeroDivisionError('''Could not find root'''		) from None

  # Precision is checked by comparing the difference of consecutive guesses
  if abs(next_guess - prev_guess		) < precision:
   return next_guess

  _UpperCamelCase:  Any    						=			next_guess


# Let's Execute
if __name__ == "__main__":
  # Find root of trigonometric function
  # Find value of pi
  print(f"""The root of sin(x) = 0 is {newton_raphson('sin(x)', 2)}""")

  # Find root of polynomial
  # Find fourth Root of 5
  print(f"""The root of x**4 - 5 = 0 is {newton_raphson('x**4 -5', 0.4 +5J)}""")

  # Find value of e
  print(
      '''The root of log(y) - 1 = 0 is ''',
      f"""{newton_raphson('log(y) - 1', 2, variable='y')}""",
  )

  # Exponential Roots
  print(
      '''The root of exp(x) - 1 = 0 is''',
      f"""{newton_raphson('exp(x) - 1', 1_0, precision=0.0_0_5)}""",
  )

  # Find root of cos(x)
  print(f"""The root of cos(x) = 0 is {newton_raphson('cos(x)', 0)}""")