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Why are trigonometric functions called periodic functions?

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A graph of the function f(x) = x cubed minus 3x plus 2 is shown on a blue background, with a red curve passing through key points. Local maximum and minimum points are marked with black dots at x equals negative 1 and x equals 1, illustrating important features of the curve. — function Plot of the cubic equation f(x) = x³ − 3x + 2. The plotted points are where changes in curvature occur.

Trigonometric functions are classified as periodic functions because their values recur at regular, predictable intervals.1

In mathematics, this occurs because these functions—such as sine and cosine—can be defined as the coordinates of a point moving along a unit circle. As the angle increases, the point eventually returns to its original position, causing the function values to repeat every 360° (or 2π radians). Because a trigonometric function yields the same value for all coterminal angles, the functions exhibit this repeating behavior with a fixed period of either 180° or 360°, depending on the specific function.23

This property makes them essential for describing periodic phenomena in science, such as the oscillations of a pendulum, the vibrations of a violin string, or the propagation of electromagnetic waves.2