Seriously? You think that's how the image would look if connected with straight line segments? With 5 sample points per division? Well, here it is for you - un-interpolated. Print it out, get out a ruler and pencil, and give it a go
What? Of course seriously! Did you think I was trolling you or something?
The peaks are the only part where the curve would be obvious in your capture, and many of them are oddly straight with harsh changes in slope. So I did what you suggested, more or less. I took your image into a paint program, drew vertical grid lines every 10 pixels (as measured for your dots display), lined up the grid lines with the non-smooth parts of the wave (they do coincide), and played around drawing lines. The peaks obviously aren't pointy enough, but If those lines just continued straight for a few more pixels then the whole thing would basically be straight line segments.
It would have been a lot clearer with a square-er aspect ratio per period, I think.
...and it looks a bit funny for a perfect sin.
There is no such animal.
I guess that's what it boils down to! I was expecting that the interpolation's synthetic sine would be pretty faithful, but I guess there's some rounding or error accumulation or whatever that causes it to flatten up at that aspect ratio. Interestingly, Teneyes' 6pt has just a couple pixels more per period, but the sine looks much better.