Welcome to MHF, Braedong! :smile:

At time x=0s, it is given that the rider is at the bottom of the wheel.

This means that the sine should have the value -1 for x=0s.

This is the case at -90 degrees.

Since the period is 10s and we start at minus a quarter of the full circle, 2.5 seconds needs to be deducted.