> 
> In my math book there are these parametric equations of the orbit/trajectory of a point $P$:
> $$\begin{cases}
> x(t)=\sin t\\
> y(t)=\sin 4t\\
> \end{cases}
> $$
> along with a graph/picture of it on the $y$ and $x$ axis.
> Could anyone explain why it follows the path it does?
> 
> 
> 

I unfortunately cant plot it on desmos or show a picture, so if anyone could do this, that would be great.

I thought about it, and since the x values are given by $sin(t)$, does this mean that the trajectory of $P$ first goes to the right, but after $sin(\pi)$ the $x$ values suddenly get negative, and the trajectory switches to the left of the $y$ axis?

So my question is in which direction does the orbit exactly go?

Thanks in advance