# Ferris Wheel (2): Modeling with Trigonometric Functions

- Author:
- Tim Brzezinski

**There are several parameters you can adjust here:**Period Number of Revs to Complete Height of Lowest Car Diameter of Wheel You can also manually enter

**y****-coordinate of the purple point. You can also move this point if you choose.**Interact with this applet for a few minutes. Then answer the questions that follow.

## 2.

**Notice how the purple point indicates a height of 380 feet. **Use the trigonometric function that appears on the right to solve for the shortest time it takes for any rider to reach this height of 380 feet. **Confirm that the approximate value of this answer matches the appropriate coordinate of this BIG PURPLE POINT. **

## 3.

**Slide the purple slider entitled "Other Solutions?"
**Note that if you continued to ride this Ferris Wheel indefinitely, **there would be INFINITELY MANY TIMES a rider's height would be 380 feet. **
**Yet why didn't we get EVERY POSSIBLE TIME VALUE when solving our equation in (2)? Explain. **

## 4.

**How can you use your answer for (2) to ALGEBRAICALLY DETERMINE values of other times for which a rider's height is 380 feet?** Explain. Then, algebraically determine the next few times for which this occurs. **Confirm that your results match with the appropriate coordinates of the other purple points. **