Vectors are generally oriented on a two dimensional coordinate system. The Cartesian plane has a horizontal axis, labeled X and a vertical axis labeled Y. Vectors in multiple-dimension coordinate systems can be split up into their component vectors. In the two-dimensional case, this results in a X-component and a Y-component.
The figure shows an example of a Force vector (F) broken into its components (Fx & Fy). When we break a vector into its components, the vector is a sum of the components:
F = Fx + Fy
To determine the magnitude of the components, we use the rules of triangles
Taking the angle between X-axis and the vector and considering the right triangle including the angle θ, we see that Fx is the adjacent side, Fy is the opposite side, and F is the hypotenuse.
So, from the rules for right triangles, we know that:
Fx / F = cosθ
Fy / F = sinθ
Fx = F cosθ
Fy = F sinθ
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