Sometimes, when we study the force acting on a body, it can be interesting to decompose it into several forces, each of them with the direction of the cartesian axis, in sucha a way the effect of all of them is equivalent to the force decomposed. As we study on the section vectors representation, on the plan OXY we get that:

$$\overrightarrow{F}=\overrightarrow{{F}_{x}}+\overrightarrow{{F}_{y}}={F}_{x}\xb7\overrightarrow{i}+{F}_{y}\xb7\overrightarrow{j}$$

Taking into account the definition of vector magnitude, the magnitude of the force $\overrightarrow{F}$ is obtained throughout the following expression:

$$F=\sqrt{{{F}_{x}}^{2}+{{F}_{y}}^{2}}$$

Throughout the definition of tangent of an acute angle we can relate the magnitudes F_{x} and F_{y} to the angle α that take place to with the half turn X positive on the following way:

$$\mathrm{tan}\left(\alpha \right)=\frac{{F}_{y}}{{F}_{x}}$$

Additionally we can relate these magnitudes to the lower angle that make $\overrightarrow{F}$ with the X axis, pointing to the sector of the system of reference in which it is located: