When do I use the cosine and sine functions when graphing the components of a vector? I have a vector $F_e$ and I would like to graph it to its corresponding $X$ and $Y$ components. I know that the $i_y$ component is negative, and there is no $i_x$ component.
$\vec{F_e} = F_x\vec{i_x} + F_y\vec{i_y}$
$\vec{F_e} = F_y\vec{(-i_y)}$
And to get there we have:
$F_{ex}=|\vec{F_{ex}}|\cos(270^\circ)$
$F_{ey}=|\vec{F_{ey}}|\sin(270^\circ)$
My question is when do we use the $\sin(\cdot)$ and when the $\cos(\cdot)$ to find its magnitude. Intuitively $\cos (270^\circ)$ equals $0$ and $\sin (270^\circ)$ equals $-1$. But why didn't we set $F_{ex}$ with $\sin (270^\circ)$. I know that the angle between the $X$ axis and the vector is $270^\circ$.

 A: If a point is at a unit distance from the origin, and it makes an angle $p$ with the x-axis, then $\cos p$ is defined as the x co-ordinate of that point. $\sin p$ is defined as the y co-ordinate of that point.
If a point is a distance $r$ from the origin and makes an angle $p$ wih the x-axis, then its x and y co-ordinates are $r \cos p$ and $r\sin p$ respectively.
Since you have to find the x-component of the force here, you have to use $|\vec{F}| \cos p$
A: So to clarify, you're just trying to

*

*plot the vector using it’s x-y components,
or

*or are you asking how to get the $X$ or $Y$ components of a vector?

If it’s # 1 it seems like you already did it since there’s no $X$ component and the $Y$ component is in the negative direction. If it’s # 2 then you're probably looking for $x=R\cos\theta$ and $y = R\sin\theta$ where $R$ is the force vectors magnitude and theta is the angle between the vector and the $X$ axis.
A: Recall the triangle law of vectors.
To find the x and y components, construct a triangle with the vector $F_e$ as the hypotenuse.
This is where trigonometry comes in- since $F_{ex}$ is the base of the triangle and $F_e$ is the hypotenuse, you can now figure out the trigonometric relation between $\theta$, $F_e$ and $F_{ex}$.
