# Semicircle periodic wave

What kind of curve is made of half circles?

My question is similar to this question except that my semicircles are not half of circles.

I want to take from $\dfrac{\pi}{6}$ portion to $\dfrac{5\pi}{6}$ of the circle.

That is instead of cutting the circle from middle $(y\ge 0)$ we cut it from $y\ge\sin(\frac{\pi}{6})$. How do i make such a periodic wave curve?

This is the formula for $y\ge0$

$sign(\sin(\dfrac{\pi x}{2r}))\sqrt{r^2-((x\mod 2r)-r)^2}$

I finally ended up with this formula. let

$A=r\sin(\theta)$

$B=r\cos(\theta)$

$S=sign(\sin(\dfrac{\pi x}{2B}))$

$M = x \mod (2B)$

Then a wave function that has the curve from a circle where $y\ge r\sin(\theta)$ would be as follows

$f(x)=S(\sqrt{r^2-(M-B)^2}-A)$

See the function on desmos