Modelling Sunrise and Sunset Times

The graphs of the sunrise and sunset times in London (U.K.) throughout the year are shown below:

Can you explain the kinks in the curve?

Accurate data for various locations can be found at

By making a simple adjustment, the sunrise and sunset times for London (U.K.) (without kinks !!!) can be modelled using the sine function.

Consider the sine function: $f(x)={a}\sin(bx+c)+d$

The project is to choose the values of the coefficients a, b, c and d to best model the annual cycle of sunrise (or sunset) times in London (U.K.).


This is one of the many Enrichment tasks on this site.
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