A cosine function is represented as: [tex]\mathbf{y = acos(bx + c) + d}[/tex]
- The period is [tex]\mathbf{\frac{2\pi}{3}}[/tex]
- The amplitude is 2
- The vertical shift is 1 unit down
(a) The period (T)
This is calculated as:
[tex]\mathbf{T = \frac{2\pi}{b}}[/tex]
From the graph, there are 3 complete rounds.
This means that: b = 3
So, we have:
[tex]\mathbf{T = \frac{2\pi}{3}}[/tex]
The period is [tex]\mathbf{\frac{2\pi}{3}}[/tex]
(b) The amplitude (A) of the cosine function
This is the height of each curve in the function
From the graph, the height of each complete round is 2.
So, we have:
[tex]\mathbf{A = 2}[/tex]
The amplitude is 2
(c) The vertical shift
In (b), we have:
[tex]\mathbf{A_1 = 2}[/tex]
The amplitude of the secant function is
[tex]\mathbf{A_2 = 3}[/tex]
So, the vertical shift is:
[tex]\mathbf{Shift = A_2 -A_1}[/tex]
[tex]\mathbf{Shift = 3-2}[/tex]
[tex]\mathbf{Shift = 1}[/tex]
The vertical shift is 1 unit down
Read more about functions at:
https://brainly.com/question/18496549
