A periodic function is a type of function that repeats its values at regular intervals, known as periods. For example, the sine and cosine functions are periodic because they repeat every 2π radians. This characteristic makes periodic functions useful in various fields, including physics and engineering, where they can model oscillations and waves. The general form of a periodic function can be expressed as f(x + T) = f(x), where T is the period. Common examples of periodic functions include trigonometric functions, square waves, and sawtooth waves. Understanding periodic functions is essential for analyzing patterns and behaviors in real-world phenomena.