Periodic function

Definition

A periodic function is a function that repeats its values in regular intervals or periods. The most common examples are the sine and cosine functions.

5 Must Know Facts For Your Next Test

1. A periodic function has a period $P$ if $f(x + P) = f(x)$ for all $x$ in the domain.
2. The smallest positive value of $P$ for which the periodic condition holds is called the fundamental period.
3. Sine and cosine functions have a fundamental period of $2\pi$.
4. The amplitude of sine and cosine functions represents the maximum value they attain from their midline.
5. The graphs of sine and cosine functions are wave-like and continuous.

Review Questions

• What is the fundamental period of the sine function?
• How do you determine if a function is periodic?
• What does the amplitude of a periodic function represent?

Related terms

Amplitude: The maximum absolute value of a periodic function from its mean position.

Frequency: The number of complete cycles a periodic function completes in a unit interval, often denoted as $\frac{1}{P}$ where $P$ is the period.

Phase Shift: A horizontal shift applied to a periodic function, changing its starting point along the x-axis.