Record your event through a series of photographs, or another appropriate method. (For example, regular water waves or, if you are using an oscilloscope, include a photo or video of the sound wave, and a copy of the audio file that you are measuring

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• Record the starting y-value of your object or event (when x = 0).

• Find the period of the object or event.

• Find the maximum and minimum y-values. You will need to pick a base point to reference from (usually this is a stationary object that you can measure from. For example, a stationary dock if measuring the tides).

• Determine the amplitude of the function.

• Determine the vertical translation of the function.

• Use the information gathered to create a function of the form f(x) = a sin (k (x−d) ) + c, and a function of the form  f(x) = a cos (k (x−d) ) + c.

• Graph your functions by hand. (Remember to include appropriate labels, scale, etc.)

• Using the functions that you have created, determine the y-value at the point x = period / 3  and    x = (5 × period ) / 6

(For example, if your period is 4π, then,   x = 4π / 3)

Be sure your submission answers the following questions as well:

1. Describe in your own words why the object or event you chose is periodic.

2. Explain your process for coming up with the functions that represent your object or event. Explain the point of reference you chose and why you chose it, how you measured or gathered the data you need, etc.

3. Explain a method you could use to verify that your functions are accurate (think about ways you have verified functions before, this may have been done in other units, or other courses).

4. Reflect on the assignment. What part of the assignment did you find most difficult? What did you find the easiest? What did you learn while working through this assignment?

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