Answer question number 17. The question is in the image.

Question

asked Sep 17, 2023 180k views

1 Answer

Matthewtole · Answer 1 · 2023-09-22T20:50:29+0000

A trigonometric function (sin or cos) can be written as

$g(x)=A\cos(\omega t)\text{ or }g(x)=A\sin(\omega t)$

Where A is the amplitude and ω is

$\omega=(2\pi)/(T)$

Where T is the period of the function.

Then, let's see the function in 20.

$g(x)=(1)/(2)\cos(4\pi x)$

The amplitude of the function 1/2, let's find the period

$\begin{gathered} 4\pi=\omega \\ \\ 4\pi=(2\pi)/(T) \end{gathered}$

Solve it for T

$\begin{gathered} T=(2\pi)/(4\pi) \\ \\ T=(1)/(2) \end{gathered}$

Therefore, the period of the function is 1/2, now we can graph the function, the parent function will be cos(x):

To graph

$g(x)=(1)/(2)\cos(4\pi x)$

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: