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:

F_x=Fcosθ_x=Fsinθ_y F x is equal to F per cosine of theta x, which is equal to F per sine of theta y

F_y=Fsinθ_x=Fcosθ_y F y is equal to F per sine of theta x, which is equal to F per cosine of theta y

F²=F_x²+F_y² F to the square is equal to Fx to the square plus Fy to the square

tanθ_x=F_y/F_x tangent of theta x is equal to fy divided by fx

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.