
'''simple docstring'''







from __future__ import annotations

from numpy import array, cos, cross, floataa, radians, sin
from numpy.typing import NDArray
def  snake_case_		(    __SCREAMING_SNAKE_CASE :			float				,				__SCREAMING_SNAKE_CASE :			float				,				__SCREAMING_SNAKE_CASE :			bool = False							):



						"""simple docstring"""





						if radian_mode:
												return [magnitude * cos(__SCREAMING_SNAKE_CASE							), magnitude * sin(__SCREAMING_SNAKE_CASE							)]
						return [magnitude * cos(radians(__SCREAMING_SNAKE_CASE							)							), magnitude * sin(radians(__SCREAMING_SNAKE_CASE							)							)]
def  snake_case_		(    __SCREAMING_SNAKE_CASE :			NDArray[floataa]				,				__SCREAMING_SNAKE_CASE :			NDArray[floataa]				,				__SCREAMING_SNAKE_CASE :			float = 10**-1							):



						"""simple docstring"""





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


if __name__ == "__main__":
							# Test to check if it works
							_lowercase			:  Union[str, Any]   							=	array(
							    [
							        polar_force(7_1_8.4, 1_8_0 - 3_0),
							        polar_force(8_7_9.5_4, 4_5),
							        polar_force(1_0_0, -9_0),
							    ]
							)

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

							assert in_static_equilibrium(forces, location)

							# Problem 1 in image_data/2D_problems.jpg
							_lowercase			:  Tuple   							=	array(
							    [
							        polar_force(3_0 * 9.8_1, 1_5),
							        polar_force(2_1_5, 1_8_0 - 4_5),
							        polar_force(2_6_4, 9_0 - 3_0),
							    ]
							)

							_lowercase			:  Union[str, Any]   							=	array([[0, 0], [0, 0], [0, 0]])

							assert in_static_equilibrium(forces, location)

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

							_lowercase			:  Union[str, Any]   							=	array([[0, 0], [6, 0], [1_0, 0], [1_2, 0]])

							assert in_static_equilibrium(forces, location)

							import doctest

							doctest.testmod()





'''simple docstring'''







def  snake_case_		(    __SCREAMING_SNAKE_CASE :			str							):



						"""simple docstring"""





						return [
						    txt[:a] + txt[a].upper() + txt[a + 1 :]
						    for a in range(len(__SCREAMING_SNAKE_CASE							)							)
						    if txt[a].isalpha()
						]


if __name__ == "__main__":
							__import__("doctest").testmod()



