Amplitude

Definition

Amplitude is the maximum absolute value of a periodic function measured from its average or equilibrium position. It represents the height of the wave peaks or troughs from the center line.

5 Must Know Facts For Your Next Test

1. The amplitude of the sine and cosine functions is always positive.
2. In $y = A\sin(Bx + C) + D$ and $y = A\cos(Bx + C) + D$, the amplitude is represented by $|A|$.
3. Amplitude affects only the vertical stretch or compression of the graph, not its period or phase shift.
4. For standard sine and cosine functions, i.e., $y = \sin(x)$ and $y = \cos(x)$, the amplitude is 1.
5. The unit circle can be used to understand how changes in amplitude affect sine and cosine graphs.

Review Questions

• What is the amplitude of the function $y = 3\sin(2x - \pi) - 4$?
• How does changing the amplitude affect a sine or cosine graph?
• Given a graph of a periodic function, how would you determine its amplitude?

Related terms

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

Frequency: The number of cycles a periodic function completes in a given interval.

Phase Shift: The horizontal displacement left or right for a periodic function.