# Components of a vector

A vector that is directed at angles to the customary coordinate axes, can be transformed into two parts. Each part is directed along the individual coordinate axes and these parts are mutually perpendicular.

This process is commonly used in problems in engineering where forces are very often acting at some angle from the coordinate axes. The component of a force parallel to the x-axis is called the x-component, the one parallel to the y-axis is the y-component, and so on.

In order to define the components of a vector such as the one presented in the figure below, basic trigonometry has to be applied as follows:

_{x}=Fcosθ_{x}=Fsinθ_{y}

_{y}=Fsinθ_{x}=Fcosθ_{y}

^{2}=F_{x}^{2}+F_{y}^{2}

_{x}=F_{y}/F_{x}

**Figure:** The components F_{x} and F_{y} of a force F. θ_{y} is the angle of the force F to the y-axis and θ_{x} is the angle to the x-axis.