A periodic function is a type of function that repeats its values at regular intervals, known as the period. For example, the function f(x) = \sin(x) has a period of 2\pi , meaning that every 2\pi units along the x-axis, the function returns to the same value. This characteristic makes periodic functions useful in various fields, including physics and engineering. Common examples of periodic functions include the sine and cosine functions, which are fundamental in trigonometry. These functions are often used to model oscillatory behavior, such as sound waves and alternating current in electrical circuits. Understanding periodic functions is essential for analyzing patterns and cycles in real-world phenomena.