# Question #e4066

Apr 17, 2017

See below

#### Explanation:

The idea is that you start at time $t = 0$ at the base of the Ferris wheel, and for practical reasons say that the radius is $r = 1$, so you start at the height $y = - 1$. Then, since you're taking trig, I think you suppose that the wheel spins with the same angular speed, so $\theta \left(t\right) = \omega t$ is the function of the angle, where $\omega$ is constant. Without loss of generality and to simplify, we can suppose that $\omega = 1$. Then we need to project see the point where we are at the time $t$ on the height of the wheel, so

$y \left(t\right) = \cos \left(t + c\right)$
where $c$ is a constant depending on the starting point. In order to set $c$, since we want $y \left(0\right) = - 1$, $\cos \left(c\right) = - 1$, hence $c = \pi$
So the function you need to draw is basically $y = \cos \left(t + \pi\right)$

graph{y=cos(x+pi) [-10, 10, -5, 5]}

in order to understand what happens see this video

The height realtive to the ground is basically the same except that you have to add the height of the center: so it is $y = \cos \left(t + \pi\right) + 1$.

graph{y=cos(x+pi) +1 [-10, 10, -5, 5]}