Changes in Period and Phase Shift of Sine and Cosine 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

Which reasons did you think of?

Revolt · Accepted Answer

The high and low points repeat in a pattern.; The cycle repeats at equal time intervals.; The swinging motion is smooth, unabrupt.

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?

Revolt · Accepted Answer

min-mid-max-mid-min

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 = ⇒ 0.748

Revolt · Accepted Answer

pi

Question 5

The pattern is that of .

Revolt · Accepted Answer

–cosine

Changes in Period and Phase Shift of Sine and Cosine Functions Answers

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