Trigonometric functions, like sine and cosine, are really helpful for looking at how Ferris wheels move! Let’s break it down:

• Height Function: We can track how high a passenger goes over time. We can use a formula like ( h(t) = r \sin(\omega t + \phi) + d ). Here’s what each part means:

  • ( r ) is the radius of the wheel (how big it is),
  • ( \omega ) is the speed at which the wheel spins,
  • ( \phi ) is how far along the spin we start (like a delay),
  • ( d ) is how high the wheel is off the ground.

• Graphing: When we graph this, it looks like waves. This graph shows how a passenger's height changes as the wheel goes around.

• Predicting Positions: By using different times in our formula, we can find out exactly where someone is on the wheel at any moment.

Overall, trigonometry helps us understand and describe how Ferris wheels move in a circular way!