I have been trying to solve a problem that came to me randomly about a week ago, and I am very close to solving it but have reached a roadblock when re-arranging the final equation to solve it. I do not believe the problem is necessary, but here is the equation (and the cosine function is using degrees not radians)
$$\frac {1-\cos\left(\dfrac {y}{2}\right)} {(\pi d)} \cdot 180c = y$$ $c$ and $d$ are just variables that I can substitute in based off of the situation.
I need to re arrange to solve for $y$. However, I seem to be unable to get the $y$ inside the cosine out without putting the other $y$ inside an arccosine.
Is there any way to solve this or is it impossible?
After plotting it on Desmos with sample data, I found three solutions: $0$, the expected solution, and some other irrational number like $496$ which is fine as the expected solution was an integer so easy to spot. So with sample data, there are $3$ solutions to this and one of them is $0$. I don't know whether this will help but I have included it just in case it does.
Thanks