



from __future__ import annotations

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






def 			lowerCAmelCase__	(					lowerCamelCase_	:	float ,lowerCamelCase_	:	float ,lowerCamelCase_	:	bool = False):





				'''simple docstring'''

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






def 			lowerCAmelCase__	(					lowerCamelCase_	:	NDArray[floataa] ,lowerCamelCase_	:	NDArray[floataa] ,lowerCamelCase_	:	float = 10**-1):





				'''simple docstring'''

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


if __name__ == "__main__":
							# Test to check if it works
							__snake_case       :	Union[str, Any]            =array(
							    [
							        polar_force(718.4, 1_8_0 - 3_0),
							        polar_force(879.54, 4_5),
							        polar_force(1_0_0, -9_0),
							    ]
							)

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

							assert in_static_equilibrium(forces, location)

							# Problem 1 in image_data/2D_problems.jpg
							__snake_case       :	Optional[Any]            =array(
							    [
							        polar_force(3_0 * 9.81, 1_5),
							        polar_force(2_1_5, 1_8_0 - 4_5),
							        polar_force(2_6_4, 9_0 - 3_0),
							    ]
							)

							__snake_case       :	Optional[Any]            =array([[0, 0], [0, 0], [0, 0]])

							assert in_static_equilibrium(forces, location)

							# Problem in image_data/2D_problems_1.jpg
							__snake_case       :	Dict            =array([[0, -2_0_0_0], [0, -1_2_0_0], [0, 1_5_6_0_0], [0, -1_2_4_0_0]])

							__snake_case       :	str            =array([[0, 0], [6, 0], [1_0, 0], [1_2, 0]])

							assert in_static_equilibrium(forces, location)

							import doctest

							doctest.testmod()






from __future__ import annotations






def 			lowerCAmelCase__	(					lowerCamelCase_	:	list[int]):





				'''simple docstring'''

				return len(set(lowerCamelCase_)) == len(lowerCamelCase_)


if __name__ == "__main__":
							import doctest

							doctest.testmod()

