I am working on a barn door tracker for taking astro photos. My drive train has a small periodic error that I'm trying to eliminate and I was hoping someone might be able to suggest a formula that would approximate what is shown in the attached image. The image shows three cycles of the error. It appears to me to be similar to a sine wave but with the upper half stretched out. It doesn't need to be exact, just something so when I subtract it out, I'll get close to a straight line. I hope that makes sense. Any assistance would be greatly appreciated.
Looks like a curtate cycloid:$C(t)=(x(t),y(t))$ where
$$ \begin{matrix}x = At-B\sin(t)\\ y = A-B\cos(t) \end{matrix}$$
for $0 < A < B$. I made the following with $A=1$, $B=4$.
To choose different values of $A,B$ and see what happens, see: https://www.desmos.com/calculator/4jl1c70nsa
The following was taken from Wolfram Mathworld: