Modeling with Periodic Functions

Question 1

Question 1

Revolt · Accepted Answer

The motion of a child on a swing is periodic because it repeats at regular time intervals. The height of the swing reaches the same maximum and minimum points in each cycle, and the movement is smooth and continuous, making it a good fit for a trigonometric model.

Question 2

The pattern is that of cosinesine–cosine–sine.

Revolt · Accepted Answer

sine

Question 3

The first decision is a choice between y = acos[b(x – h)] + k and y = asin[b(x – h)] + k.Starting at the green point, which general pattern does the graph follow? mid-max-mid-min-midmid-min-mid-max-midmax-mid-max-mid-minmin-mid-max-mid-min

Revolt · Accepted Answer

mid-max-mid-min-mid

Question 4

Recall that h, the phase shift, is any value of x that occurs at the beginning of a cycle. The green point begins the –cosine cycle. What value of x corresponds to this point?h = [___]

Revolt · Accepted Answer

pi

Question 5

The y-value for the midline is equal to max y + min y(max y + min y)/2max y – min y(max y – min y)/2.

Revolt · Accepted Answer

(max y + min y)/2

Question 6

The vertical shift, k, is the amount every y-value is shifted when compared to the basic sine or cosine function. In other words, it is the same y-value as the midline. For the equation of this graph, k = [___].

Revolt · Accepted Answer

2

Question 7

What is the amplitude of this graph?[___]

Revolt · Accepted Answer

2

Question 8

The period is .

Revolt · Accepted Answer

2.244

Question 9

The formula for period is StartFraction 2 pi Over b EndFraction . Use the value of the period, 2.244, to solve for the value of b, rounded to the nearest tenth:b =

Revolt · Accepted Answer

2.8

Modeling with Periodic Functions Answers

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