Question

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

f (x) = 3 cos (TX) – 2
Express the answer in fraction form.

Answer 1

Frequency =
`(1)/(2)`

Explanation:

We are given the following function and we are to find its frequency:

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

We know that the standard form of cosine function is
`y=Acos (Bx)+c`

where
`A` is the amplitude,
`B=\frac{2\pi}{\text{Period}}` while
`c` is the mid line.

Frequency is given by:

`F=(1)/(P)` where
`F` is frequency and
`P` is the period.

Finding period by comparing the given function:

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

`Period - B = \pi`

Substituting B to get:

`\pi =\frac{2\pi}{\text{Period}}`

`\text{Period}=(2\pi)/(\pi)=2`

So, Period = 2.

Since frequency is
`(1)/(P)`, therefore

Frequency =
`(1)/(2)`