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Suppose that a force with a magnitude of 42.6 N is exerted at an angle of 36 degrees with the horizontal. This force would be the same as having two forces which are exerted at ____ and ____.
(Note: Numbers are randomized numbers and likely different from the numbers listed here.)
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Definition of Vector Component
A vector component is a projection of a vector onto the horizontal or vertical axis.
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The components of a vector are often represented on a diagram by constructing a right triangle about the vector such that the vector is the hypotenuse of the right triangle. The components are then the legs of the right triangle. (You have likely seen such diagrams and might make an effort to sketch one now.) If the vector is a northwest vector, then it has components stretching west and north. The west and north components are simply the west and north legs of the triangle which has been created from the northwest vector.
Trigonometric functions can be used to determine the precise magnitude of the legs of these triangles. If the angle Θ is the counterclockwise angle of rotation from the eastern axis and the vector, then the x-component can be calculated using the cosine function; the y-component can be calculated using the sine function.
Ax= A • cosine Θ
Ay= A • sine Θ
where Θ = counterclockwise angle rotation of vector A from the east.
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