




'''simple docstring'''

from __future__ import annotations

from numpy import array, cos, cross, floataa, radians, sin
from numpy.typing import NDArray


def 		__magic_name__    (	__UpperCAmelCase,      __UpperCAmelCase,      __UpperCAmelCase = False	)		->					list[float]:

					'''simple docstring'''

					if radian_mode:
										return [magnitude * cos(__UpperCAmelCase	), magnitude * sin(__UpperCAmelCase	)]
					return [magnitude * cos(radians(__UpperCAmelCase	)	), magnitude * sin(radians(__UpperCAmelCase	)	)]


def 		__magic_name__    (	__UpperCAmelCase,      __UpperCAmelCase,      __UpperCAmelCase = 10**-1	)		->					bool:

					'''simple docstring'''

					snake_case_									=				cross(__UpperCAmelCase,      __UpperCAmelCase	)
					snake_case_									=				sum(__UpperCAmelCase	)
					return abs(__UpperCAmelCase	) < eps


if __name__ == "__main__":
							# Test to check if it works
							a  :				Tuple									=  array(
							    [
							        polar_force(718.4, 180 - 30),
							        polar_force(879.54, 45),
							        polar_force(100, -90),
							    ]
							)

							a  :				NDArray[floataa]									=  array([[0, 0], [0, 0], [0, 0]])

							assert in_static_equilibrium(forces, location)

							# Problem 1 in image_data/2D_problems.jpg
							a  :				Union[str, Any]									=  array(
							    [
							        polar_force(30 * 9.81, 15),
							        polar_force(215, 180 - 45),
							        polar_force(264, 90 - 30),
							    ]
							)

							a  :				List[Any]									=  array([[0, 0], [0, 0], [0, 0]])

							assert in_static_equilibrium(forces, location)

							# Problem in image_data/2D_problems_1.jpg
							a  :				List[Any]									=  array([[0, -2000], [0, -1200], [0, 1_5600], [0, -1_2400]])

							a  :				str									=  array([[0, 0], [6, 0], [10, 0], [12, 0]])

							assert in_static_equilibrium(forces, location)

							import doctest

							doctest.testmod()





"""simple docstring"""







from __future__ import annotations

from numpy import array, cos, cross, floataa, radians, sin
from numpy.typing import NDArray


def      lowercase			(				A_  ,   A_  ,   A_ = False       )->      list[float]:
  '''simple docstring'''







  if radian_mode:
    return [magnitude * cos(A_       ), magnitude * sin(A_       )]
  return [magnitude * cos(radians(A_       )       ), magnitude * sin(radians(A_       )       )]


def      lowercase			(				A_  ,   A_  ,   A_ = 10**-1       )->      bool:
  '''simple docstring'''







  a						:		NDArray[floataa]      							=			cross(A_  ,   A_       )
  a						:		float      							=			sum(A_       )
  return abs(A_       ) < eps


if __name__ == "__main__":
 # Test to check if it works
 __lowercase    					=      array(
     [
         polar_force(7_18.4, 180 - 30),
         polar_force(8_79.54, 45),
         polar_force(100, -90),
     ]
 )

 __lowercase    					=      array([[0, 0], [0, 0], [0, 0]])

 assert in_static_equilibrium(forces, location)

 # Problem 1 in image_data/2D_problems.jpg
 __lowercase    					=      array(
     [
         polar_force(30 * 9.81, 15),
         polar_force(215, 180 - 45),
         polar_force(264, 90 - 30),
     ]
 )

 __lowercase    					=      array([[0, 0], [0, 0], [0, 0]])

 assert in_static_equilibrium(forces, location)

 # Problem in image_data/2D_problems_1.jpg
 __lowercase    					=      array([[0, -2000], [0, -1200], [0, 15600], [0, -12400]])

 __lowercase    					=      array([[0, 0], [6, 0], [10, 0], [12, 0]])

 assert in_static_equilibrium(forces, location)

 import doctest

 doctest.testmod()






