Periodic functions.

Definition

Periodic functions are functions that repeat their values at regular intervals, known as periods. Trigonometric functions like sine and cosine are classic examples of periodic functions.

5 Must Know Facts For Your Next Test

1. The period of a function is the length of the interval over which the function repeats.
2. $\sin(x)$ and $\cos(x)$ both have a period of $2\pi$.
3. A function $f(x)$ is periodic if there exists a positive number $P$ such that $f(x + P) = f(x)$ for all $x$ in the domain of $f$.
4. The amplitude of a periodic function is half the distance between its maximum and minimum values.
5. Periodic functions can be represented using Fourier series, which break down any periodic function into sums of sines and cosines.

Review Questions

• What is the period of $\sin(x)$?
• How would you determine if a given function is periodic?
• Explain how amplitude relates to periodic functions.

Related terms

Amplitude:

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

Frequency: Frequency is the number of times a periodic function repeats itself within a unit interval.

Fourier Series: A mathematical tool used to express any periodic function as a sum of simple sine and cosine waves.