Question

For the function Y=-3Cos4x +6 State the Amplitude, Period, Frequency, and Vertical Shift.

Answer 1

Amplitude = -3

Period =
`(2\pi)/(4)=(\pi)/(2)`

Frequency =
`(1)/(\pi/2)=(2)/(\pi)`

Vertical Shift = 6.

Explanation:

Consider the function:

`y=A\ sin (B(x+C))+D`

Here,

A = amplitude; It is the measure of how high is the peak from the center line.

2π/B = period; A period is the distance between one peak to the next.

C = phase shift; it represents how far the function is shifted horizontally from the initial point.

D = vertical shift; it represents how far the function is shifted vertically from the initial point.

The frequency of a function is the number of times something happens per unit time.

`\text{Frequency}=(1)/(Period)`

The function provided is:

`y=-3\ cos\ 4x+6`

On comparing the provided function with the general one it can be determined that:

Amplitude = -3

Period =
`(2\pi)/(4)=(\pi)/(2)`

Frequency =
`(1)/(\pi/2)=(2)/(\pi)`

Vertical Shift = 6.