Problem
A bicycle wheel with a $70-\mathrm{cm}$ diameter is moving at a speed of 24 centimeters per second. A small stone is stuck in the wheel tread. A trigonometric function can model the height y of the stone above the ground as a function of the time $t$. This function has a period of $\frac{5 \pi}{4}$ and an amplitude of 70 . Which function could model this situation?
Solution
Step 1 ：Find the angular frequency: \(\omega = \frac{2\pi}{T} = \frac{2\pi}{\frac{5\pi}{4}} = \frac{8}{5}\)
Step 2 ：Write the possible functions: \(y(t) = 70\sin(\frac{8}{5}t)\) or \(y(t) = 70\cos(\frac{8}{5}t)\)
Step 3 ：\boxed{y(t) = 70\sin(\frac{8}{5}t) \text{ or } y(t) = 70\cos(\frac{8}{5}t)}
