> how close to a sine wave is the Daylight line?

It's as close as the Earth's orbit is to a perfect circle and that the shapes of the earth and sun are to perfect spheres and as the axis of the earth has no wobble and no precession and the sun's rays are truly parallel and and there is no drag in space sapping energy from the dynamics and general relativity effects are sent to zero and so on.

Once everything is perfectly circular and simple and Euclidean, then it does become a perfect sinewave. Then the sinewave has period = 1 year, the amplitude is symmetric by latitude, and it's pretty easy to derive.

All the above (and more) all intorduce measurable errors from the perfect sinewave.