phase shift

**Chr2010** · December 13th 2010, 04:22 PM

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

**Prove It** · December 13th 2010, 04:30 PM

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

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

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

Your calculation of $\displaystyle b$ is incorrect.

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

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

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

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

**Chr2010** · December 13th 2010, 05:05 PM

The ferris wheel is 2.5metres above the ground.

**Chr2010** · December 13th 2010, 05:07 PM

how did u determine the period is 2?

**Prove It** · December 13th 2010, 05:20 PM

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...

**Chr2010** · December 13th 2010, 05:29 PM

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

**Prove It** · December 13th 2010, 06:04 PM

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

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

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

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