1. ## phase shift

A ferris wheel has a diametre of 50.5 metre and takes 2 min to complete a rotation. The lowest point is 2.5 metres from the ground.

I need to write an equation to represent the graph. So far I have y=25.25sin(3x-b)+27.75.

How do I calcualte the phase shift? Is my equation completely off?

Thanks,
Christine

2. If you had a sine graph of the form $\displaystyle \displaystyle y = a\sin{(bx - c)} + d$,

Your amplitude $\displaystyle \displaystyle a = 25.25$ is correct.

Your vertical translation $\displaystyle \displaystyle d = 27.75$ is correct.

Your calculation of $\displaystyle \displaystyle b$ is incorrect.

The period is $\displaystyle \displaystyle 2$, so you should have $\displaystyle \displaystyle 2 = \frac{2\pi}{b}$

$\displaystyle \displaystyle b = \frac{2\pi}{2} = \pi$.

So you should have $\displaystyle \displaystyle y = 25.25\sin{(\pi x - c)} + 27.75$.

To evaluate the phase shift, you need a coordinate on the graph. Do you know the height when the ferris wheel starts?

3. The ferris wheel is 2.5metres above the ground.

4. how did u determine the period is 2?

5. Because it says it takes 2 mins to complete a rotation.

And I know it's 2.5m above the ground. I'm asking, what is the height of the basket when it starts? It's the height of one particular basket that is being graphed...

6. oh... no it does not... your help is greatly appreciated!

7. Then I expect you can assume it starts at the bottom, where the height is 2.5m.

So you have a point $\displaystyle \displaystyle (x, y) = (0, 2.5)$.

Substitute this into your equation and you can solve for $\displaystyle \displaystyle c$.