Place x number of points equidistant from each other on a circle segment circumference So I have a circle segment, a 90 degrees part of a circle, so 1/4 of the circle. I know the radius and I want to place an x number of points spread out evenly on the circumference. How can I achieve that using a formula?
Picture

Use the fact that a circle is determined by $x=r\cos\theta$, $y=r\sin\theta$ where $r$ is the radius of the circle, 
$0\leq\theta<2\pi$, and $\theta$ is the angle made by the x-axis and the line connecting the point on the circle and the origin. In the way that you want, the formula is $$x_k=r\cos\frac{k\pi}{2(n+1)},~y_k=r\sin\frac{k\pi}{2(n+1)}$$ where $n$ is the number of points and $(x_k,y_k)$ is the $k^{th}$ point on the segment (and thus $1\leq k\leq n$). This places all the points in the first quadrant. To offset the points, merely add a constant term to the arguments of the sine and cosine.
e.g. $$x_k=r\cos\bigg(\frac{k\pi}{2(n+1)}-\frac{\pi}{2}\bigg),~y_k=r\sin\bigg(\frac{k\pi}{2(n+1)}-\frac{\pi}{2}\bigg)$$
rotates the points a quarter-turn clockwise, moving them into the $4^{th}$ qudrant as shown in the picture you gave.
