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April 9th, 2019, 09:26 PM  #1 
Newbie Joined: Apr 2019 From: WA Posts: 1 Thanks: 0  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 merrygoround). Watch the video “MerryGoRound.” (MerryGoRound descriptive transcript) Assume the camera is placed 6 feet from the center of the merrygoround and the diameter of the merrygoround 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. MerryGoRound 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 merrygoround 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 merrygoround forward. If we pretend the merrygoround 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 merrygoround. [00:20] The video then rewinds and replays at half speed from the beginning. https://players.brightcove.net/11262...=5556623829001 (Video link for carousel movement) 
April 10th, 2019, 08:02 AM  #2 
Math Team Joined: Jul 2011 From: Texas Posts: 2,887 Thanks: 1506 
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 merrygoround at the origin, then the distance from the camera to any point on the edge of the merrygoround 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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based, bottom, carousel, function, make, movement, question, shown, trig 
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