Question

Part 1: Write mathematical equations of sinusoids.

1. The following sinusoid is plotted below. Complete the following steps to model the curve using the cosine function.

a) What is the phase shift, c, of this curve? (2 points)
b) What is the vertical shift, d, of this curve? (2 points)
c) What is the amplitude, a, of this curve? (2 points)
d) What is the period and the frequency factor, b, of this curve? (2 points
e) Write an equation using the cosine function that models this data set. (5 points)

2. The following points are a minimum and a maximum of a sinusoid. Complete the following steps to
model the curve using the sine function.
(4.5, 2), (1.5, 22)


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Answer 1

The phase shift of the curve is π/4 to the right, the vertical shift is 3 units up, the amplitude is 2 units, the period is 2π units, and the equation using the cosine function is y(x) = 2cos(x-π/4)+3.

Step-by-step explanation:

a) The phase shift, represented by the letter c, of the curve can be determined by finding the horizontal displacement of the curve from its original position. In this case, the phase shift is π/4 to the right.

b) The vertical shift, represented by the letter d, of the curve can be found by determining the vertical displacement of the curve from the x-axis. In this case, the vertical shift is 3 units up.

c) The amplitude, represented by the letter a, of the curve is the maximum distance between the curve and the x-axis. In this case, the amplitude is 2 units.

d) The period, represented by the letter T, is the length of one complete cycle of the curve. The frequency factor, represented by the letter b, is the reciprocal of the period. In this case, the period is 2π units and the frequency factor is 1/(2π) units.

e) The equation using the cosine function that models this data set is y(x) = 2cos(x-π/4)+3.