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

a. f(x) = −2 sin(x − π/6 ) + 4

b. f(x) = 4 sin 12x − 2

c. f(x) = 4 sin(x − π/6 ) − 2

d. f(x) = −2 sin 12x + 4

B). f(x) = 4 sin 12x − 2.

Step-by-step explanation:

Given : A sine function with an amplitude of 4, a period of pi/6 , and a midline at y = −2.

To find : What function best represents a sine function.

Solution : We have  amplitude of 4, a period of pi/6 , and a midline at y = −2.

Standard form of sin function : y = a sin[ b(x-h)] + k.

Where, a = amplitude

= time period.

b =

b = 12x

k = vertical displacement. , h = 0

Then Substitute the values  a =4 , b = 12x k = -2 in standard form

y = 4 sin 12x - 2.

Therefore, B). f(x) = 4 sin 12x − 2.

-2

7 - 9 = -2

reversed:

-2 + 9 = 7