Thanks to Zac at squareCircleZ for pointing out the dawn and dusk graphs at Gaisma as real-life examples of approximate sine graphs.

In fact the true time of noon appears to oscillate slightly with a 6 month period so that the Tokyo graphs are modelled pretty well by 6+1.5sin(2pix/12)-0.15sin(2pix/6) & -6-1.5sin(2pix/12)-0.15sin(2pix/6).

(**Update**: thanks to zac also for pointing out in the comment below that I should either have used cosines or have said “where x is the number of months since the spring equinox”)

It will be neat to be able to give Gaisma as a source of reference data for the hours of daylight modelling examples in my precalculus classes.

I’m glad you found it useful, Alan.

I wanted to find a minute to model them, but I see you have done it already!

However, surely they are cosine-based graphs, rather than sine?