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April 9th, 2019, 09:26 PM   #1
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Question: Make Trig Function based on carousel's movement (shown at bottom)

In this exploration, you have the chance to use what you have learned about trigonometric functions and their graphs by building a function that models a real periodic situation (a merry-go-round).

Watch the video “Merry-Go-Round.” (Merry-Go-Round descriptive transcript)
Assume the camera is placed 6 feet from the center of the merry-go-round and the diameter of the merry-go-round is 6 feet. Build a trigonometric function that models the distance (feet) of the rider from the camera as a function of time (seconds). Be sure to use function notation to express your function model.
Draw the graph of your trigonometric function. Be sure to show labeled axes on your graph.
Identify the domain of your function. Explain what the domain has to do with the video you watched.
Identify the range of your function. Explain what the range has to do with the video you watched.
What is the period of your function? Explain what the period has to do with the video you watched.
What is the midline of the graph of your function? Explain what the midline has to do with the video you watched.

Merry-Go-Round Video—Descriptive Text
[00:00] Words on the screen read “distance from camera,” and underneath that, “regular speed.” A man is
shown climbing on top of a merry-go-round at a playground. A timer on screen says ready, set, go, and
then begins counting the seconds.
[00:04] The man uses his foot to propel the merry-go-round forward. If we pretend the merry-go-round is
a clock, he starts at 6:00. At 1 second he is at 12:00; at 2 seconds, 2:00; 3 seconds, 4:00; 4 seconds, 9:00.
[00:11] At 7 seconds he is back around to 6:00. 7 seconds, 9:00; 8 seconds, 11:00; 9 seconds, 3:00, 10
seconds, 6:00; 11 seconds, 9:00.
[00:16] At 12 seconds he reaches 12:00 and stops the merry-go-round.
[00:20] The video then rewinds and replays at half speed from the beginning. (Video link for carousel movement)
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April 10th, 2019, 08:02 AM   #2
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The video shows 3.5 revolutions in a negative angular direction in 12 seconds. You should be able to determine an angular speed, $\omega$, from that information.

If you place the camera at coordinates (6,0) with the center of the merry-go-round at the origin, then the distance from the camera to any point on the edge of the merry-go-round can be determined using the law of cosines.

Note the angular position of any such point on the edge will be $\theta(t) = -\omega t$ since $\theta(0) = 0$

See what you can get done from here.

Last edited by skeeter; April 10th, 2019 at 09:01 AM.
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