Thread: Finding the equation of a sine function

A carnival Ferris wheel with a radius of 9.5m rotates once every 10s. The bottom of the wheel is 1.2m above the ground. Find the equation of the sine function that gives the rider's height above the ground, in metres, as a function of time,in seconds, with the rider starting at the bottom of the wheel.
The answer in the back of the book is y=9.5sin36(x-2.5)+10.7

I understand where most of the equation comes from, I just don't understand where the -2.5 comes from.

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.