Question

What function best represents a sine function with an amplitude of 4, a period of pi over 6, and a midline at y = −2?

Answer 1

f(x) = 4 sin 12x − 2

Explanation:

Answer 2

Let us suppose the sine function is in the form

`y=A\sin(Bx)+D`

We have been given that the amplitude is 4. It means we have

`A=4`

Now, period is given by
`(\pi)/(6)`

Thus, we have

`(2\pi)/(B) =(\pi)/(6) \\ \\ B=12`

Now, we have been given that the mid line is
`y=-2`. Hence, we have

`D=-2`

Therefore, the sine function is given by

`y=4\sin(12x)-2`