Think of an example of something that follows a cyclical pattern .There are many examples used in this module, but you must provide an example NOT used in this unit. If you cannot come up with an example, Google it. Remember, "cyclical" is something that goes in cycles or occurs in a repeating pattern.

My example of something that follows a cyclical pattern is: /1

If you were to graph this cycle what would be the independent variable? /2 What would be the dependent variable?

What is the highest point on your graph? What is the lowest point? /3

Explain.

How long does your example take to undergo one complete cycle and /2

start over again? Explain

Where does your graph begin/start? Explain. /1

Sketch a graph of this example. Your graph must be clear and include /4 these key elements:

Title, is a proper sinusoidal function, clear/legible (1.5 marks)

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Labelled x & y Axis' ( mark)

Start point ( mark)

Maximum/Minimum ( mark)

Period ( mark)

Median ( mark)

Determine the sinusoidal equation of your example in the form: /4

.

What is the domain and range of your function? Explain. /2

When comparing two different sinusoidal functions that are in the form

we noticed that:

Function 1 has triple the amplitude of function 2

Function 2 has half the period and double the median value of function 1

Create two possible sinusoidal functions that are in the form /4

that satisfy the conditions stated above.

Sinusoidal Function 1: .

Sinusoidal Function 2: .

Consider a Ferris wheel, which loads passengers at a height of 0.5 meters above ground and carries them to a height of at most 12 meters.

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How would you increase the amplitude of the function? Explain. /1

How would you decrease the b-value of the function? Explain. /1

A paddle wheel on a boat (see image below) has a diameter of 5 meters and takes 180 seconds to complete one revolution. As the wheel begins to turn, a barnacle attaches to the wheel at its lowest point, which is 0.5 meters below the surface of the water.

Create a table of values that describes the height of the barnacle on /2

the outer edge of the wheel during the first 12 minutes of the boat ride.

Below is a template table of values.

-hint the table is 10x2

the length of the table is 2 square and the width is 10

Time

Height

Use your table of values to write a sinusoidal regression equation /2

that models the height of the barnacle as a function of time. (Round

to the nearest tenth).

How does the radius of the paddle wheel relate to the parameters of /2

your equation? Explain

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The barnacle falls off the wheel after 22.5 minutes. Use your regression /2

equation to predict the height of the barnacle when it falls of the wheel,

to the nearest tenth of a meter.

Determine the total time within the first rotation that the barnacle is /2

at least 2 meters above the surface of the water, rounded to the nearest

tenth of a minute