A bicycle wheel is spinning in place. The vertical position of a point on the wheel, in inches, is described by the function \(f(t) = 13.5\sin(5 \boldcdot 2\pi t) + 20\). Time, \(t\), is measured in seconds.

1. What is the meaning of 13.5 in this context?
2. What is the meaning of 5 in this context?
3. What is the meaning of 20 in this context?

Each expression describes the vertical position, in feet off the ground, of a carriage on a Ferris wheel after \(t\) minutes. Which function describes the largest Ferris wheel?

Which trigonometric function has a period of 5?

Here is a graph of \(y=\cos(x)\).

1. Sketch a graph of \(\cos(2x)\).

   

2. How do the two graphs compare?

Here is a table that shows the values of functions \(f\), \(g\), and \(h\) for some values of \(x\). 

1. Use the table to determine the value of \(a\) in the equation \(g(x)=f(ax)\).
2. Use the table to determine the value of \(b\) in the equation \(h(x)=f(bx)\).