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 $270^\circ$.

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 $270^\circ$.

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:

$F_{ex}=|\vec{F_{ex}}|\cos(270^\circ)$

$F_{ex}=|\vec{F_{ex}}|\sin(270^\circ)$

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 $270^\circ$.

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 $270^\circ$.