A trigonometric function (sin or cos) can be written as
[tex]g(x)=A\cos(\omega t)\text{ or }g(x)=A\sin(\omega t)[/tex]
Where A is the amplitude and ω is
[tex]\omega=\frac{2\pi}{T}[/tex]
Where T is the period of the function.
Then, let's see the function in 20.
[tex]g(x)=\frac{1}{2}\cos(4\pi x)[/tex]
The amplitude of the function 1/2, let's find the period
[tex]\begin{gathered} 4\pi=\omega \\ \\ 4\pi=\frac{2\pi}{T} \end{gathered}[/tex]
Solve it for T
[tex]\begin{gathered} T=\frac{2\pi}{4\pi} \\ \\ T=\frac{1}{2} \end{gathered}[/tex]
Therefore, the period of the function is 1/2, now we can graph the function, the parent function will be cos(x):
To graph
[tex]g(x)=\frac{1}{2}\cos(4\pi x)[/tex]
We have to modify the amplitude to 1/2, therefore
Now, we have to modify the period, the function will be period in 1/2, then
Final answer:
