Modeling with Periodic Functions

Question 1

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 2

The pattern is that of cosinesine–cosine–sine.

Revolt · Accepted Answer

sine

Question 3

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 4

What is the amplitude of this graph?[___]

Revolt · Accepted Answer

2

Question 5

The period is .

Revolt · Accepted Answer

2.244

Question 6

Question 6

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 7

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 8

Question 8

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 9

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?

Revolt · Accepted Answer

min-mid-max-mid-min

Question 10

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

Modeling with Periodic Functions Answers

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