Midline

Definition

The midline of a periodic function is the horizontal axis that runs through the middle of the graph, equidistant from its maximum and minimum values. It represents the average value of the function over one period.

5 Must Know Facts For Your Next Test

1. The midline can be found by averaging the maximum and minimum values of the function.
2. For $y = A \sin(Bx + C) + D$ or $y = A \cos(Bx + C) + D$, the midline is given by $y = D$.
3. The midline does not change when the amplitude or period of the sine or cosine function changes.
4. Shifting a sine or cosine graph vertically will change the position of its midline.
5. In real-world applications, the midline often represents a central baseline around which periodic phenomena oscillate.

Review Questions

• How do you determine the equation of the midline for a sine or cosine function?
• What happens to the midline if you add a constant to a sine or cosine function?
• If a periodic function has maximum value 10 and minimum value -2, what is its midline?

Related terms

Amplitude: The amplitude is half the distance between the maximum and minimum values of a periodic function.

Period: The period is the length of one complete cycle of a periodic function.

Phase Shift: $\text{Phase shift}$ refers to horizontal displacement along the x-axis in graphs of trigonometric functions.