Question

What are the amplitude, period, and midline of `f(x)=-7sin(4x-n)+27`?

Answer 1

`7 "units", pi/2, 27 "units"`

Explanation:

The Amplitude of any simple sinusoidal wave is the coefficient of the function of `x`.

Amplitude is a measure of distance and so cannot be negative, only a positive value.

In this example, the amplitude would be `7` units.

The period of a sinusoidal function is `2pi` divided by the coefficient of the `x`. In this case, the coefficient of `x` is 4.

`therefore "Period" =(2pi)/4`
`=pi/2`

The midline of a simple sinusoidal wave is the constant at the end of the function. In the case of this example it would be 27 units.