# Thread: Finding period, frequency and hor shift?

1. ## Finding period, frequency and hor shift?

Hey folks,

Here is the question that I am struggling with.

I am riding a Ferris Wheel. My height h in feet above the ground at any time t (in seconds) can be modeled by the following equation:

h=28sin((pi*t)/12 - pi/2) +30

What is the period, frequency, and horizontal shift of this function. Also, what are the minimum and maximum heights above the ground?

2. $\displaystyle h=28sin\left(\frac{\pi t}{12} - \frac{\pi}{2}\right) +30 \Rightarrow h=28sin\left(\frac{\pi }{12}(t-6)\right) +30$

Now consider
$\displaystyle h=28sin\left(\frac{\pi }{12}(t-6)\right) +30$

max hight will be 28+30, min height will be -28+30.

frequency = $\displaystyle \frac{2\pi}{\frac{\pi}{12}} = 24$

3. Originally Posted by pickslides
frequency = $\displaystyle \frac{2\pi}{\frac{\pi}{12}} = 24$
$\displaystyle Period=\frac{2\pi}{\frac{\pi}{12}} = 24$

$\displaystyle frequency = \frac{1}{Period}=\frac{1}{24}$

Horizontal Shift = 6 units Right.

4. Wouldn't the horizontal shift be $\displaystyle pi/24$right? I factored out the $\displaystyle pi/12$ and and got $\displaystyle 28sin pi/12(x-(pi/24)) +30$

So would it by $\displaystyle pi/24$to the right?

5. if you factored out $\displaystyle \frac{\pi}{12}$ then how can there be $\displaystyle \pi$ remaining in your horizontal shift component?

6. If I exapnd what you have above I get this

$\displaystyle \frac{\pi}{12}\left(x-\frac{\pi}{24}\right) = \frac{\pi x}{12}x-\frac{\pi^2}{288}$

This is no where near what you started with.