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

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 $\frac{\pi}{6}$

Thus, we have

$\frac{2\pi}{B} =\frac{\pi}{6} \\ \\ B=12$

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

$D=-2$

Therefore, the sine function is given by

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

Answer 2

Answer:

f(x) = 4 sin 12x − 2

Step-by-step explanation: