Question

What is the frequency of the function f(x)?

f(x)=3cos(πx)−2



Express the answer in fraction form.

Enter your answer in the box.

Answer 1

The frequency is
`(1)/(2)` Hz

Explanation:

Sinusoid Function

The cosine and sine functions are generally called sinusoids because of their characteristic oscillatory behavior.

The general cosine function is expressed as

`y(x)=A\cos(\omega x+\phi)+B`

Where A is the amplitude, ω is the angular frequency, Ф is the phase shift and B is the midline or vertical shift.

We are given the function:

`f(x)=3\cos(\pi x)-2`

The coefficient of x is the angular frequency, thus

`\omega=\pi`

Since

`\omega=2\pi f`

Where f is the frequency, then

`2\pi f=\pi`

Simplifying:

`f=(1)/(2)`

The frequency is
`(1)/(2)` Hz