Just a disclosure I am not a huuuuge math person. I am trying to find points on circles if I was to travel some distance around those circles.
For example, if I have this circle:
$$\left(x-0\right)^{2}+\left(y-0\right)^{2}=2^{2}$$
This circle's center is at (0,0) and the "top" of the circle is at (0,2). Let's say I now wanted to travel from the top, in a clockwise direction around the circle. Let's say I wanted to only go 1/5th of the circumference, what would be the x and y coordinates for where I would stop?
In practice, any circle I use would always be centered at (0,0) but could be any size and the distance I would travel would also vary (sometimes 1/5th, sometimes 1/2, etc).
As mentioned previously, I am not a big math person, but I did try googling how to do this and was unsuccessful. The concept of arc lengths looked promising, but I couldn't understand how the central angle works in my case.
Best Answer
The central angle is this case is $\theta=2\pi/5$. Whatever the fraction of the circumference you want to travel, in angle is the same fraction out of $2\pi$.
If your circle has radius $r$, $r=2$ in this case, and you measure the angle in the clockwise direction, from the vertical line, the position on the circle is given by $$x=r\sin\theta\\y=r\cos\theta$$ If the center of the circle is not at $(0,0)$, then $$x=r\sin\theta+x_c\\y=r\cos\theta+y_c$$