Model contextual situations using trigonometric functions (Part I).
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Given below are two graphs that show the populations of foxes and rabbits in a national park over a 24 month period.
a. Explain why it is appropriate to model the number of rabbits and foxes as trigonometric functions of time.
b. Find an appropriate trigonometric function that models the number of rabbits, $${r(t)}$$, as a function of time, with $$t$$ in months.
c. FInd an appropriate trigonometric function that models the number of foxes, $$f(t)$$, as a function of time, with $$t$$ in months.
Foxes and Rabbits 3, accessed on Feb. 26, 2018, 4:39 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.
Have students participate in the Matching Graphs and Functions activity on page T-6 in Representing Trigonometric Functions from MARS.
Representing Trigonometric Functions from the Classroom Challenges by the MARS Shell Center team at the University of Nottingham is made available by the Mathematics Assessment Project under the CC BY-NC-ND 3.0 license. Copyright © 2007-2015 Mathematics Assessment Resource Service, University of Nottingham. Accessed Feb. 26, 2018, 4:40 p.m..
Modified by The Match Foundation, Inc.?
The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.
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A Ferris wheel is 50 meters in diameter and rotates once every three minutes. The center axle of the Ferris wheel is 30 meters from the ground.
a. Using the axes below, sketch a graph to show how the height of a passenger will vary with time. Assume that when the wheel starts rotating when the passenger is at the bottom.
b. A mathematical model for this motion is given by the formula
$${h=a+b\mathrm{cos}ct}$$ where $$h$$= the height of the car in meters
$$t$$= the time that has elapsed in minutes
$${a, b, c}$$ are constants
Find values for $$a$$, $$b$$, and $$c$$ that will model this situation.
Representing Trigonometric Functions from the Classroom Challenges by the MARS Shell Center team at the University of Nottingham is made available by the Mathematics Assessment Project under the CC BY-NC-ND 3.0 license. Copyright © 2007-2015 Mathematics Assessment Resource Service, University of Nottingham. Accessed Feb. 26, 2018, 4:40 p.m..