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Applications of Sinusoidal Functions (Round 2)

Applications of Sinusoidal Functions (Round 2). MHF4UI Friday November 16 th , 2012. 2=1?. 1. Applications of Sinusoidal Functions Example 1.

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Applications of Sinusoidal Functions (Round 2)

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  1. Applications of Sinusoidal Functions (Round 2) MHF4UI Friday November 16th, 2012

  2. 2=1? 1

  3. Applications of Sinusoidal Functions Example 1 Off the end of a pier, the depth of the water changes with the tide. The depth (d) in metres can be represented as a function of time (t) in hours after midnight. a) Determine the amplitude, period phase shift and vertical shift of the function.

  4. Applications of Sinusoidal Functions Example 1 Off the end of a pier, the depth of the water changes with the tide. The depth (d) can be represented as a function of time (t) in hours after midnight. b) Use the info to sketch the function over a 24 hour interval.

  5. Applications of Sinusoidal Functions Example 1 Off the end of a pier, the depth of the water changes with the tide. The depth (d) can be represented as a function of time (t) in hours after midnight. c) Determine when the depth will be 8metres in the first 12 hours To determine when the depth of 8m will occur we can sub the depth into the equation and solve for t 8 Let Therefore the depth we be 8metres at about 7:14am and 10:46am in the first 12hours.

  6. Applications of Sinusoidal Functions Example 2 A Ferris wheel with a 50m radius rotates once every 90 seconds. Passengers get on at the lowest point of the ride (2m off the ground). • Sketcha graph showing height above the ground through the first two cycles.

  7. Applications of Sinusoidal Functions Example 2 A Ferris wheel with a 50m radius rotates once every 90 seconds. Passengers get on at the lowest point of the ride (2m off the ground). b) Write an equation to express height as a function of time. for a negative cosine function Therefore,

  8. Applications of Sinusoidal Functions Example 2 A Ferris wheel with a 50m radius rotates once every 90 seconds. Passengers get on at the lowest point of the ride (2m off the ground). c) Calculate the height of the ride after 24s. Therefore the height of a ride after 24 seconds is about 57.23 metres.

  9. Applications of Sinusoidal Functions Example 2 A Ferris wheel with a 50m radius rotates once every 90 seconds. Passengers get on at the lowest point of the ride (2m off the ground). d) Between what times will the Ferris wheel be 82m or higher in the first revolution? Therefore the ride is 82metres or higher between about 31.72seconds and 58.28seconds of the first revolution.

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