# Calculate circle by circular sector area and yearn

I'm in great despair right now. I got the task to solve a circles values by given circular yearn and circular sector area.

The values are not specific but I used Area $$A=8$$ and yearn $$y=3$$ for calculations.

I tried to integrate the function of yearn $$y=2\sin(\alpha/2)$$ into $$A=\frac{r^2\pi\alpha}{360}$$

and got $$f(x)=\left(\frac{y}{2\sin(\alpha/2)}\right)^2\cdot\frac{\pi\alpha}{360}-A$$

if I insert values it shows correct answers, so it seems correct.

The problem: If I try to calculate the roots (which will represent the value for alpha and is the key for more values)

with the newton method, I get an infinite number of roots.

I'm working on it for two hours now, my head is burning and I can't find any appropriate solution.

I welcome any help given!!!

• I don't understand the problem definition. What is circular yearn in this case? And what do you mean by "solve a circles values"? Could you draw a picture or explain it better? – Matti P. Sep 11 at 9:50