What is a midline point anyway? Can you be more context specific about how cosine & sine relate to this midline point?

Thank you for that question. The OP is about midpoints. Midlines are not defined is metric spaces, example $\mathbb{R}^2$. qie

Midpoints are defined in terms of two other points. So a question about

*midpoints* on a sine curve is meaningless.

I am prepared to argue that $M_s: \left(\frac{\pi}{2},1\right)$ is the midpoint of the graph $\left\{(x,\sin(x): 0\le x\le\pi\right\}$

Clearly, $M_s$ is both equally distant from $(0,0)~\&~(\pi, 0)$ in an ordinary sense as well as the arc-lengths.

However, as this question is posted in

*basic algebra* arc-length is not applicable.

Likewise, $M_c: \left(\frac{\pi}{2},0\right)$ is the midpoint of the graph $\left\{(x,\cos(x): 0\le x\le\pi\right\}$.