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Ferris Wheel (2): Modeling with Trigonometric Functions

This applet graphs the height of an person riding a Ferris Wheel vs. time. 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.
1. Hit the refresh (recycle) button to reset it. Then slide the black slider all the way to the right.


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.


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.


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.