Modeling with Periodic Functions Assignment 1

The y-value for the midline is equal to The vertical shift, k, is the amount everyy-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,

(max y + min y)/2 k=4

What is the amplitude of this graph?

2

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

2.244 b=2.8

What do the graphs of sine and cosine have in common with the swinging you see?

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

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

The first decision is a choice betweeny = acos[b(x - h)] + k andy = asin[b(x - h)] + k.Starting at the green point, which general pattern does the graph follow? The pattern is that of ________.

min-mid-max-mid-min -cosine