suppose that you want to model the height of a rider on a ferris wheel as a function of time, $t$, in…

Brief Explanations:

The standard cosine function $y = A\cos(Bx - C)+D$ has a maximum value at $x = 0$. The standard sine function $y=A\sin(Bx - C)+D$ has a value of $y = D$ at $x = 0$. When the rider is at the bottom of the Ferris - wheel at $t = 0$, we want a function that starts at its minimum value. The cosine function reflected about its mid - line starts at its minimum value. The unreflected cosine starts at its maximum, the unreflected sine starts at its mid - line value, and the reflected sine starts at its mid - line value in the opposite direction of change compared to what we need.

Answer:

the cosine function reflected about its midline