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.

b. an equilateral triangle inscribed in a circle

step-by-step explanation:

we are given the figure of two circles having a triangle inside.

now, we know that,

"when a figure is lying inside an another figure, then the outside figure is known as circumscribed figure and the figure lying inside is referred to as the inscribed figure".

as we see that, the circles are containing the triangle completely.

thus, the circles are the circumscribed figures and the triangle is the inscribed figure.

hence, we get, 'an equilateral triangle is inscribed in a circle'.