study guides for every class

that actually explain what's on your next test

Midline

from class:

Algebra and Trigonometry

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.

congrats on reading the definition of midline. now let's actually learn it.

ok, let's learn stuff

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?
© 2024 Fiveable Inc. All rights reserved.
AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.
Glossary
Guides