Ferris Wheel (2): Modeling with Trigonometric Functions

This applet graphs the height of an person riding a Ferris Wheel vs. time. [br][br][b]There are several parameters you can adjust here: [/b][br][br]Period[br]Number of Revs to Complete[br]Height of Lowest Car[br]Diameter of Wheel[br][br]You can also manually enter [i][b][color=#9900ff]y[/color][/b][/i][color=#9900ff][b]-coordinate of the purple point. You can also move this point if you choose. [br][/b][br][/color]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.
2.
[b][color=#9900ff]Notice how the purple point indicates a height of 380 feet. [/color][/b]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. [b][color=#9900ff]Confirm that the approximate value of this answer matches the appropriate coordinate of this BIG PURPLE POINT. [/color][/b]
3.
[color=#9900ff][b]Slide the purple slider entitled "Other Solutions?"[br][br][/b][/color]Note that if you continued to ride this Ferris Wheel indefinitely, [b][color=#9900ff]there would be INFINITELY MANY TIMES a rider's height would be 380 feet. [/color][/b][br][br][b]Yet why didn't we get EVERY POSSIBLE TIME VALUE when solving our equation in (2)? Explain. [/b]
4.
[b][color=#9900ff]How can you use your answer for (2) to ALGEBRAICALLY DETERMINE values of other times for which a rider's height is 380 feet?[/color][/b] Explain. Then, algebraically determine the next few times for which this occurs. [b][color=#9900ff]Confirm that your results match with the appropriate coordinates of the other purple points. [/color][/b]
Close

Information: Ferris Wheel (2): Modeling with Trigonometric Functions