Well basicly to calculate a x component of a force vector you use:

Fx = Fxcosß

Note that:

x in Fx is subscript

x in Fxcosß stands for multiplication

ß is angle between positive part of the x axis and the direction of the vector (measuring counterclockwise).

For y component you use:

Fy = Fxsinß

When you have multiple force vectors you use:

Fx = F1xcosß1 + F2xcosß2+ F3xcosß3 + ... + Fnxcosßn

Fy = F1xsinß1 + F2xsinß2 + F3xsinß3 + ... + Fnxsinßn

These two formulas are great because you don't need to change + and -, sin and cos are going to tell you whether it's + or -.

For example:

You have two forces:

F1 = 10 N ß1=30°

F2 = 15 N ß2 = 200°

Fx = 10xcos30° + 15xcos200°

Fy = 10xsin30° + 15xsin200°

Fx = 8,66 + (-14,1)

Fy = 5 + (-5,13)

Fx = -5,44 N

Fy = -0,13 N

Since you got both components negative your vector will be in the third quadrant.

To get the intensity (module, scalar whatever you want to call it) of that vector use:

|FR| = square root (Fx^2 + Fy^2)

Note that |FR| has an arrow above F to indicate that it's a vector, R is subscript, | | means module.

|FR| = 5,4416 N

To calculate the direction (angle ßR, resulting angle) you can use:

tg ßR = Fy/Fx

tg ßR = 0,239

ßR = 1,369°

IMPORTANT:

You must add another 180° to get correct angle, since you know your vector is in III. quadrant.

So your vector is:

FR = 5,4416 N

ßR = 181,369°