Question

below is the graph of a trigonometric function. it has a minimum point at \\((-2, -5.2)\\) and an amplitude of \\(1.1\\).

what is the midline equation of the function?

Explanation:

Identify given values

The minimum value of the trigonometric function is \(y_{\text{min}} = -5.2\).
The amplitude of the function is \(A = 1.1\).

Relate midline to minimum

The midline of a trigonometric function is the horizontal line halfway between its maximum and minimum values.
Mathematically, the minimum value is related to the midline \(y = k\) and the amplitude \(A\) by:

$$y_{\text{min}} = k - A$$

Solve for the midline

Substitute the known values into the equation:

$$-5.2 = k - 1.1$$

$$k = -5.2 + 1.1$$

$$k = -4.1$$

Formulate the final equation

The midline is a horizontal line, which is represented by the equation \(y = k\).
Thus, the equation of the midline is:

$$y = -4.1$$

Answer:

\(y = -4.1\)